Since every polygon can be divided into triangles, the angle sum property can be extended to find the sum of the angles of all polygons. But anyway, regardless of how we do it, if we just reason . In any given polygon, whether there are 3 sides or 16 sides, the sum of all exterior angles is always 360^@. 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. When a quadrilateral is inscribed in a circle, it is known as a cyclic quadrilateral. % The formula for calculating the sum of interior angles is \(\left({n 2} \right) \times 180^\circ \) or \(\left({2n 4} \right) \times 90^\circ \) where n is the number of sides. Half of this is the angle on a straight line, which is 180. You also have the option to opt-out of these cookies. Both the figures given above are quadrilaterals. 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. Given that CDA = 84^{\circ} calculate the value of a . Show that the two quadrilaterals below are similar. 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.

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