Angles in a quadrilateral add to equal 360^{\circ} . No tracking or performance measurement cookies were served with this page. Firstly, a rather long and sophisticate term regular quadrilateral signifies a simple and familiar square. . We use the "Sum of Interior Angles Formula" to find an unknown interior angle of a polygon. y=180-(3\times50-25) Interior Angles: Definition, Theorem, Formula, Types, Examples In a quadrilateral ABCD ,which is not a trapezium.It is known that What is the measure of the exterior angle of quadrilateral? So yes, even for concave quadrilaterals, the sum of the exterior . When the sides of a quadrilaterals are extended and the exterior angles are produced. x+30+x+5x+20+2x+40=9x+90, 98^{\circ}, 95^{\circ}, 110^{\circ}, 57^{\circ}, We use essential and non-essential cookies to improve the experience on our website. Before explaining what the angle sum property of a quadrilateral is, let us first understand what quadrilaterals are. According to the Angle sum property of quadrilaterals, the sum of the interior angles is 360. On adding both equations \((1)\) and \((2)\), we have, \((\angle ADC + \angle DAC + \angle DCA) + (\angle ABC + \angle BAC + \angle BCA) = 180^\circ + 180^\circ \), \(\Rightarrow \angle ADC + (\angle DAC + \angle BAC) + (\angle BCA + \angle DCA) + \angle ABC = 360^\circ \ldots (3)\). !J%Bdvh5$LTgig4c/i$$4cTtjU,:'^bKC,r#S`8LKmj1tcD\CzqlD=5` y\Q^^^QvpcGsd%F6J4cw&Sl/{|J#O${q rudaduC$snc1NNF1>Ko8gYc1!*e}gYP4cL&DDNg@"EA0,i1n;:y/ \1c[bak>7c|X"c15,.|||mK?m}1G)XV_YR,;r_>}y7s)h?%"m;&vlIHj?1)1+c9J-i}361D]+Q;#0pyf For example, if an interior angle of a quadrilateral is 60, then its corresponding exterior angle will be, 180 - 60 = 120. 8 0 obj B A C = C D E. Therefore, C D E = 75 . As x = 63 we can find the value for the remaining angles in the kite by substituting the value onto each angle: So we have the four angles: 45, 126, 126, and 63 . What is Water Pollution? \(g\) is . The sum of the interior angles of a quadrilateral are equal to 360. With any other shape, you can get much higher values. Therefore, the 4th angle = 360 - 240 = 120. 4. As x=24, the measure of each of the exterior angles would be 24 degrees, 48 degrees, 72 degrees, 96 degrees, and 120 degrees. It may be a flat or a plane figure spanned across two-dimensions. Good morning, Chanchal. Let us prove that the sum of all the four angles of a quadrilateral is \(360^\circ \). Any shape with four sides including all squares and rectangles are quadrilaterals. $Ys(_lx}}SjvK,1vJmc1\Xn)Dr7^tVY85mDsBJ/VR,%Z24cL'^qeduv|pKDK1c y5>DdNyM-b'JPFYpi9#}1ACQT!g According to the angle sum property of a polygon, the sum of the interior angles of a polygon can be calculated with the help of the number of triangles that can be formed in it. The angle sum property of a quadrilateral states that the sum of all interior angles of a quadrilateral is \(360^\circ \). Create a new GeoGebra file and do some investigating to informally test your hypotheses! Take a square for example. In a quadrilateral, if the sum of two angles is 200, find the measure of the other two equal angles.Ans: Given, the sum of two angles is \(200^\circ \).Let us say the measure of equal angles is \(x\).We know the sum of the interior angles of a quadrilateral is \(360^\circ \).We can say, \(x + x + 200^\circ = 360^\circ \Rightarrow 2x = 360^\circ 200^\circ \Rightarrow x = \frac{{160^\circ }}{2} = 80^\circ \)Therefore, the measure of equal angles is \(80^\circ \).Q.4. Ans: B A C = C D E (exterior angle of a cyclic quadrilateral is equal to the interior angle at the opposite vertex) And we are given that B A C = 75 . There are also angles in quadrilaterals worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if youre still stuck. Example 2: Determine each exterior angle of the quadrilateral. When a quadrilateral is inscribed in a circle, it is known as a cyclic quadrilateral. Definition, Types, Preservation, Examples, Natural Resources Definition, Types, and Examples, Water Scarcity Definition, Causes, Issues, Examples, Human Resources Characteristics, Population Density, Factors Affecting. If we observe the figure given above, we can see that the exterior angle and interior angle form a straight line, and hence, they make a linear pair. Example 2: If 3 interior angles of a quadrilateral are given as 77, 98, and 110, find the 4th angle. The opposite angles of a cyclic quadrilateral are always supplementary. This formula can also be used to find the interior angle if the corresponding exterior angle is given. Half of this is the angle on a straight line, which is 180. 4. Use the information below to calculate the value of b . Polygons: Exterior Angles - GeoGebra Finding the exterior angle of a quadrilateral - YouTube There are different types of quadrilaterals such as the square, rectangle, rhombus, and so on. When we draw a draw the diagonals to the quadrilateral, it forms two triangles. The sum of all the exterior angles of a polygon is always 360 degrees. Octagon (8 Sides) An Octopus has 8 tentacles. Quadrilateral Angles Calculator - Symbolab What is the measure of each exterior angle of a regular quadrilateral (180(n 2))}, N = 180n 180(n 2) N = 180n 180n + 360N = 360. DAB + CDA = 180^{\circ} because they are co-interior so \theta=112^{\circ}. 545 That's not a very precise way of describing them, but hopefully you can see from my picture what I mean by that. Salakot (version 2) Wallpaper p6m. Since both of them form a linear pair, their sum is always equal to 180. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. 180 x 2 = 360, so there are 360 degrees in the interior of a quadrilateral. >QNE# * UDSoI*:Yay;d6M#%D-9e 6!qPnLa=ocW$k](um#hk^+ Angles, Quadrilaterals. In case, if the quadrilateral is a square or a rectangle, then all its exterior angles will be 90 each. Firstly, a rather long and sophisticate term regular quadrilateral signifies a simple and familiar square. In a quadrilateral, n = 4, so after substituting the value of n as 4, we get, Sum = (4 2) 180 = 360. Sum of the exterior angles of a polygon (video) | Khan Academy stream stream The exterior angles of a quadrilateral have measures of 72 - Socratic In this article we have provided a detailed definition of this property with proof. ABCD is a quadrilateral. Decagon (10 Sides) In this article we . The sum of the interior angles of a polygon can be calculated with the formula: S = (n 2) 180, where 'n' represents the number of sides of the given polygon. ABCD is an irregular quadrilateral where BE is a straight line through C . As the sum of angles in a triangle is 180 , we can add two lots of 180 together, making the angle sum of a quadrilateral equal to 360 . So, \(n=4\)Thus, using the formula of angle sum property of a polygon, we get, Interior angle sum \(=(4-2) \times 180^{\circ}=2 \times 180^{\circ}=360^{\circ}\). Which is always a rhombus? These triangles are formed by drawing diagonals from a single vertex. Therefore, the total angle sum of the quadrilateral is 360. Please read our, How to find missing angles in a quadrilateral, Example 3: parallelogram with one interior angle (form and solve), Example 4: parallelogram with one interior angle (form and solve), Practice angles in a quadrilateral questions, Two pairs of supplementary angles (co-interior), Vertically opposite angles at the intersection of the diagonals, One pair of opposite angles are congruent, All the properties of a rectangle and a rhombus, Angles at the intersection of the diagonals are, One pair of parallel sides, therefore two pairs of supplementary angles (co-interior), One pair of congruent angles (if symmetrical). y=55^{\circ}, y=180-(140-2x)=2x+40\\ (a) It is formed by joining four non-collinear points. The interior opposite angle is 75. Polygon is a closed, connected shape made of straight lines. Angles in Quadrilaterals Worksheets - Math Worksheets 4 Kids Hence, Sum of the exterior angles of any polygon is 360. A: Sum of the exterior of the polygon or convex quadrilateral is 360. Thus, the exterior angle measures are 180 - a, 180 - b, 180 - c, and 180 - d, Adding these together gives (180 - a) + (180 - b) + (180 - c) + (180 - d) = 720 - (a + b + c + d), Since a + b + c + d = 360, this is equal to 720 - 360, which equals, The intersecting lines at the four vertices form angles adding to 360 degrees. To prove: Sum of the interior angles of a triangle is \(180^\circ \)Let us consider a \(\Delta ABC\). Angles in a quadrilateral are the four angles that occur at each vertex within a four-sided shape; these angles are called interior angles of a quadrilateral. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. Number of sides = Sum of all exterior angles of a polygon nValue of one pair of side = 360 degree 60 degree = 6Therefore, this is a polygon enclosed within 6 sides, that is hexagon. Interior and exterior angles - Angles in triangles and quadrilaterals All rights reserved, Angle Sum Property of a Quadrilateral: Definition, Properties, Proofs, All About Angle Sum Property of a Quadrilateral: Definition, Properties, Proofs, JEE Advanced Previous Year Question Papers, SSC CGL Tier-I Previous Year Question Papers, SSC GD Constable Previous Year Question Papers, ESIC Stenographer Previous Year Question Papers, RRB NTPC CBT 2 Previous Year Question Papers, UP Police Constable Previous Year Question Papers, SSC CGL Tier 2 Previous Year Question Papers, CISF Head Constable Previous Year Question Papers, UGC NET Paper 1 Previous Year Question Papers, RRB NTPC CBT 1 Previous Year Question Papers, Rajasthan Police Constable Previous Year Question Papers, Rajasthan Patwari Previous Year Question Papers, SBI Apprentice Previous Year Question Papers, RBI Assistant Previous Year Question Papers, CTET Paper 1 Previous Year Question Papers, COMEDK UGET Previous Year Question Papers, MPTET Middle School Previous Year Question Papers, MPTET Primary School Previous Year Question Papers, BCA ENTRANCE Previous Year Question Papers, IB Security Assistant or Executive Tier 1, SSC Selection Post - Higher Secondary Level, Andhra Pradesh State Cooperative Bank Assistant, Bihar Cooperative Bank Assistant Manager Mains, Bihar Cooperative Bank Assistant Manager Prelims, MP Middle School Teacher Eligibility Test, MP Primary School Teacher Eligibility Test. Let us consider an example to find the missing angle $\angle x$ in the following quadrilateral. Q.2. <> elmtv-803-1214d-6. The measures of opposite angles in a quadrilateral sum to 1 8 0 . The formula for calculating the measure of an interior angle of a polygon is given by: \({\text{Interior}}\,{\text{angle}}\,{\text{of}}\,{\text{a}}\,{\text{polygon}} = \frac{{{\text{ Sum of interior angles }}}}{{{\text{ Number of sides }}}}\). Exterior Angles of a Quadrilateral - Ask Professor Puzzler So, we have. Hence, we have the sum of the exterior angle of a polygon is 360. Angles in a quadrilateral add up to 360^{\circ} . Nonagon (9 Sides) Think Nonagon is a "Nine-agon". These angles share a common arm and lie next to each other. This property helps in finding the unknown angles of quadrilateral. Calculate the missing angle for the following parallelogram: Calculate the missing angle for the following quadrilateral. That's just a little terminology you could see there. Necessary cookies are absolutely essential for the website to function properly. Wallpaper cmm. Show that the two quadrilaterals below are similar. Note that when we talk about the exterior angles of a quadrilateral, we're not talking aboutallthe angles formed by the sides that lie outside the quadrilateral. We can also write this as. Sum of Interior Angles and Exterior Angles of Polygons - Hatsudy 1)BJg9c1.1K |NE"B#s Z[*CO\YYoH.CzYVX/.MOz;_JgT*OA L+( =~@f] $7[wc.W_)l9rG#Z)dFD~q*4|sqVE?w@_u Ypg n 0-qvCL1>T/As5$,AsPjRX-@_ctR]*tjHeBV#u|tIG]F Polygon is a closed, connected shape made of straight lines. Scroll down the page for more examples and solutions on how to find interior and exterior angles of quadrilaterals. 9PavB(%OfYc1"DqNTiK-["gXO-=G2Pc1} W2! Example: Find the 4th interior angle of a quadrilateral if the other 3 angles are 85, 90, and 65 respectively. The theorem related to the opposite angles of a cyclic quadrilateral says that," The opposite angles in a cyclic quadrilateral are supplementary, i.e., the sum of the opposite angles is equal to 180". Therefore, the exterior angle is 112. The sum of the interior angles of any quadrilateral is 360 . \SXVfZx ^`\ T71c.4Ko,(":"KH]bTxxJX,XK8xc15c)MC%:WpQQl"DAn]"9vKr`^tj]1c Interior angles in a triangle add up to 180. x = 46 The sum of all exterior angles of any polygon is always 360 degrees. For example, one theorem related to the opposite angles of a cyclic quadrilateral says that," The opposite angles in a cyclic quadrilateral are supplementary, i.e., the sum of the opposite angles is equal to 180". What are the Effects of Acid Rain on Taj Mahal? In the cyclic quadrilateral, side B D is produced to E and B A C = 75 . In \(\Delta ABC\) given above, a line is drawn parallel to the side \(BC\) of \(\Delta ABC.\). Good morning, Chanchal. Formation, Life Span, Constellations, What is Air Pollution? Diagonally opposite angles in a parallelogram are equal: One pair of diagonally opposite angles in a kite are the same size. Since the straight angle measures \(180^\circ \),\(\angle PAQ = 180^\circ \), \(\angle PAB + \angle BAC + \angle CAQ = 180^\circ .\left( 1 \right)\), As \(PQ\|BC,\,AB\) is a transversal, and the alternate interior angles are equal.\(\therefore \angle PAB = \angle ABC\left(2\right)\). Or you could just say, look, if I have the exterior angles right over here, it's equal to the sum of the remote interior angles. The important points related to the angles of a polygon are: 1. Free Quadrilateral Angles Calculator - calculate the angles of a quadrilateral step by step They make a quadrilateral in the following arrangement An interior angle and exterior angle are supplementary. Trapezium A trapezium has two parallel sides. You can control the size of a colored exterior angle by using the slider with matching color. We know that the exterior angle and the corresponding interior angle of a quadrilateral form a linear pair. The formula for calculating the measure of an exterior angle is given by, \({\text{Exterior}}\,{\text{angle}}\,{\text{of}}\,{\text{a}}\,{\text{polygon}} = \frac{{360^\circ }}{{{\text{ Number of sides }}}}\). The sum of interior angles in a quadrilateral is 360. Check out the following pages related to the angles of quadrilateral. This formula is used when an interior angle of a quadrilateral is known and the value of the corresponding exterior angle is required. We can prove this using the angle sum of a triangle. 3x + 300 = 360. Why is it Important to Separate Religion from State? Angles in a Quadrilateral question. You can control the size of a colored exterior angle by using the slider with matching color. Angles on a straight line add to equal 180^{\circ} . For example, if an interior angle of a quadrilateral is 50, then its corresponding exterior angle will be, 180 - 50 = 130. We are not permitting internet traffic to Byjus website from countries within European Union at this time. Moreover, we discuss the sum property of a polygon and triangle as well. All rights reserved.Third Space Learning is the Exterior angle = 180 - Interior angle. Leading AI Powered Learning Solution Provider, Fixing Students Behaviour With Data Analytics, Leveraging Intelligence To Deliver Results, Exciting AI Platform, Personalizing Education, Disruptor Award For Maximum Business Impact, Copyright 2023, Embibe. In that case, the formula will be, Interior angle = 180 - Exterior angle. What is Quadrilateral? Properties, Types and Examples of Quadrilaterals Note: For the quadrilateral & pentagon, the last two applets work best . If 3 angles of a quadrilateral are known, then the 4th angle can be calculated using the formula: 360 - (Sum of the other 3 interior angles), The sum of interior angles of a quadrilateral = Sum = (n 2) 180, where 'n' represents the number of sides of the given polygon. What is. &>>A1ttzFqKC9MgD9 ('26c;2g$2X@Qb}/rf`"G4i'! vertical angles are congruent (vertical angles are the angles across from each other formed by two intersecting lines), The blue dashed line is a diagonal of the quadrilateral, The sides of the quadrilateral have been extended to form exterior angles, The purple arcs indicate angles which are opposite (vertical) to the interior angles of the quadrilateral. Human heart functions throughout the life Types of Blood Vessels: We all have blood vessels inside our bodies and underneath our skin. Interior and exterior angles. 3 Subtract the angle sum from \pmb {360} 360360. Each angle is supplementary to an exterior angle. Therefore, the 4th interior angle is 117. So, the sum of the interior angles of a quadrilateral is 360 degrees. For example, if 3 angles of a quadrilateral are given as 67, 87, and 89, we can find the 4th angle using the sum of the interior angles. The following diagrams show that the sum of interior angles of a quadrilateral is 360 and the sum of exterior angles of a quadrilateral is 360. Chanchal from Muktsar asks if we could prove that in a quadrilateral the sum of exterior angles is 360. Here, the angle x should be equal to 60 and y should be equal to 105 due to co-interior angles in parallel lines. Given that CDA = 84^{\circ} calculate the value of a . y=180-(3\times50-25) 3. The lines forming the polygon are known as the edges or sides and the . Let us see how this is applicable in quadrilaterals. Crack NEET with ease and boost your scores, Human Heart Definition, Diagram, Anatomy and Function, Procedure for CBSE Compartment Exams 2022, CBSE Class 10 Science Chapter Light: Reflection and Refraction, Powers with Negative Exponents: Definition, Properties and Examples, Square Roots of Decimals: Definition, Method, Types, Uses, Diagonal of Parallelogram Formula Definition & Examples, Phylum Chordata: Characteristics, Classification & Examples, CBSE to Implement NCF for Foundation Stage From 2023-24, Interaction between Circle and Polygon: Inscribed, Circumscribed, Formulas. Relationship between Angles at the Circumference and Arcs. A quadrilateral has four sides, four angles, and four vertices. This formula can also be used to find the interior angle if the corresponding exterior angle is given. Chanchal from Muktsar asks if we could prove that in a quadrilateral the sum of exterior angles is 360. Angles of Quadrilateral Formula. The opposite angles are those angles that are diagonally opposite to each other. and more. Co-interior angles add to equal 180^{\circ}, Diagonally opposite angles in a parallelogram are equal, All angles correspond and the sides are enlarged by a scale factor of 2. Sources, Causes, Prevention, CBSE Class 8 Social Science Revision Notes, Company Rule Expands From Trade to Territory, Blue Rebellion And After | Class 8 History, Planning For Development Overview and Examples. There are various types of quadrilaterals and all of them follow the angle sum property of quadrilaterals. This adjacent sides of a square are perpendicular, this angle is #90^o#. If the side of a triangle is extended, the angle formed outside the triangle is the exterior angle. Q.5. We know that a triangle is a polygon with three sides, so, \(n=3\).Thus, using the formula of calculating the sum of interior angles, we get the sum of interior angles of a triangle asInterior angle sum \(\; = \left( {3 2} \right) \times 180^\circ \; = 180^\circ \). There are two triangles. What is common about the measures of the exterior angles of any one of these polygons? By Internal Angles of a Quadrilateral Theorem, "The sum of the measures of the interior angles of a quadrilateral is 360". Simplify. ABCD is a trapezium. Observe the following figure to understand the difference between the interior and exterior angles of a quadrilateral. This fact is a more specific example of the equation for calculating the sum of the interior angles of a polygon: \[\text {Sum of interior . A quadrilateral can be divided into two triangles by a diagonal. Examples of polygons are triangle, quadrilateral, pentagon, hexagon, etc. Q.1. 2. Parallelogram, Trapezoid, Rectangle, or Square? Angle sum is one of the properties . There are four interior angles in a quadrilateral and they add up to a sum of 360. 6. Interior angles in a quadrilateral add up to 360. 2 Add all known interior angles. Firstly we have to find interior angles x and y.DAC + x = 180 {Linear pairs}110 + x = 180 x = 180 110 x = 70 Now,x + y + ACB = 180 {Angle sum property of a triangle}70+ y + 50 = 180 y + 120 = 180y = 180 120y = 60, Secondly now we can find exterior angles w and z.w + ACB = 180 {Linear pairs}w + 50 = 180w = 180 50w = 130, Now we can use the theorem exterior angles sum of a polygon,w + z + DAC = 360 {Sum of exterior angle of a polygon is 360}130 + z + 110 = 360240 + z = 360z = 360 240z = 120, Chapter 2: Linear Equations in One Variable, Chapter 9: Algebraic Expressions and Identities, Chapter 13: Direct and Inverse Proportions, Chapter 1: Crop Production and Management, Chapter 2: Microorganisms: Friend and Foe, Chapter 4: Materials: Metals and Non-Metals, Chapter 7: Conservation of Plants and Animals, Chapter 8: Cell Structure and Functions, Chapter 10: Reaching The Age of Adolescence, Chapter 14: Chemical Effects Of Electric Current, Chapter 2: From Trade to Territory: The Company Establishes Power, Chapter 6: Weavers, Iron Smelters and Factory Owners, Chapter 7: Civilising the Native, Educating the Nation, Chapter 9: The Making of the National Movement: 1870s-1947, Chapter 6: Understanding Our Criminal Justice System, Chapter 2: Land, Soil, Water, Natural Vegetation, and Wildlife Resources, Class 8 NCERT Solutions - Chapter 3 Understanding Quadrilaterals - Exercise 3.4, Class 8 NCERT Solutions - Chapter 3 Understanding Quadrilaterals - Exercise 3.1, Class 8 NCERT Solutions - Chapter 3 Understanding Quadrilaterals - Exercise 3.2, Class 8 RD Sharma Solutions - Chapter 16 Understanding Shapes Quadrilaterals - Exercise 16.1 | Set 1, Class 8 RD Sharma Solutions- Chapter 16 Understanding Shapes Quadrilaterals - Exercise 16.1 | Set 2, Class 8 NCERT Solutions- Chapter 3 Understanding Quadrilaterals - Exercise 3.3, Class 8 RD Sharma Solutions - Chapter 17 Understanding Shapes Special Types Of Quadrilaterals - Exercise 17.1 | Set 1, Class 8 RD Sharma Solutions - Chapter 17 Understanding Shapes Special Types Of Quadrilaterals - Exercise 17.1 | Set 2, Class 8 RD Sharma Solutions - Chapter 17 Understanding Shapes Special Types Of Quadrilaterals - Exercise 17.2 | Set 1, Class 8 RD Sharma Solutions - Chapter 17 Understanding Shapes Special Types Of Quadrilaterals - Exercise 17.2 | Set 2. Sum of interior angles = (n 2) 180, where 'n' represents the number of sides of the given polygon. The interior angles of a quadrilateral always sum up to 360. If the side of a triangle is extended, the angle formed outside the triangle is the, interior angle + two other interior angles = 180, exterior angle = two other interior angles. The sum of angles in a triangle is equal to 180 . In the quadrilateral above, one of the angles marked in red color is right angle. Read about our approach to external linking. 2.1 Reason Why Sum of Interior Angles Increases by 180 for Each Additional Side; 2.2 The Sum of All Exterior Angles of a Polygon Is 360; 3 Exercises: Calculating the Angles of a Polygon Do you think water in Chennai is available and affordable by all? One to one maths interventions built for KS4 success, Weekly online one to one GCSE maths revision lessons now available. x1r:v8rv;qz2cN\w-'CpvR';Wiq=~H$$ The Basic Quadrilateral: Quadrilaterals - TheProblemSite.com Secondly, an exterior angle is formed by a side and a continuation of an adjacent side. But anyway, regardless of how we do it, if we just reason . BCD=5x=100^{\circ} . Label this line as \(PQ\). "Exactly! Learn more at http://www.doceri.com y=55^{\circ}. Polygons - Math is Fun exterior angle and its corresponding interior angle form a linear pair, the measure of the interior angle is 180 - 45 or 135. The word quadrilateral is derived from the two Latin words: quadri means four and latus means sides. Here, 360 - 290 = 70 360 290 = 70. Prepare your KS4 students for maths GCSEs success with Third Space Learning. Similarly, as \(PQ||BC\) and \(AC\) is a transversal, \(\angle CAQ = \angle ACB\quad \ldots ..(3)\). One of the exterior angles of a triangle is 100. The maximum angle is 360. ABCD is an isosceles trapezium. 1 Proof Sum of Interior Angles of a Triangle Is 180. We're not including the purple angles, and we're also not including the angles opposite the red ones. Quadrilateral Angles Sum Property - Theorem and Proof - BYJU'S Four matchsticks are dropped on the floor. %PDF-1.5 VpI.4I% E |"hgb%*VyV7QZR(,PMahtWi0_M#8 This means that is a cyclic quadrilateral, and we can use the angle properties of a cyclic quadrilateral to help us find the unknown angle. Because the sum of the angles of each triangle is 180 degrees. Now, we will subtract this sum from 360, that is, 360 - 243 = 117. Substituting them in equation \((3)\) we have, \(\angle A D C+\angle D A B+\angle B C D+\angle A B C=360^{\circ}\). We can check the solution by adding these angles together. Pentagon (5 Sides) The "Pentagon" in Washington DC has 5 sidesHexagon (6 Sides) Honeycomb has Hexagons. 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