Geometry Concepts: Interior and Exterior Angles in Polygons

Explore the properties of interior and exterior angles in polygons like regular hexagons, quadrilaterals, triangles, and more. Understand how to calculate angles and sums accurately to solve geometric problems.

• Geometry Concepts
• Polygons
• Interior Angles
• Exterior Angles
• Geometric Properties

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Uploaded on Oct 01, 2024 | 0 Views

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1. Starter B C ABCDE is a regular hexagon with centre O. Use what you know about angle notation to write down the values of the below. 120 30 60 30 D A O 60 60 E F = 90 = 60 = 60 Find ABC ADC BAC CAD = 120 = 60 = 30 = 30 ACD ODE EOD

2. Interior angles A quadrilateral has 4 sides. It can be split into 2 triangles. The sum of the angles of a quadrilateral = 2 x 180 = 360 . p q r p + q + r + s = 360 s

3. Interior angles A pentagon has 5 sides. It can be split into 3 triangles. The sum of the interior angles of any pentagon = 3 x 180 = 540 q p p + q + r + s + t = 540 r s t

4. Exterior angles b a Exterior angles of a polygon add to 360 . c a + b + c + d + e = 360 e d At each vertex: interior angle + exterior angle = 180

5. Answers Name of regular polygon Equilateral triangle Square Pentagon Hexagon Heptagon Octagon Nonagon Decagon n-sided polygon Number of Sides Size of exterior angle Sum of all interior angles Size of interior angle 3 360 3 = 120 1 x 180 = 180 180 3 = 60 4 5 6 7 8 9 10 360 4 = 90 360 5 = 72 360 6 = 60 360 7 = 51.4 360 8 = 45 360 9 = 40 360 10 = 36 2 x 180 = 360 3 x 180 = 540 4 x 180 = 720 5 x 180 = 900 6 x 180 = 1080 7 x 180 = 1260 8 x 180 = 1440 360 4 = 90 540 5 = 108 720 6 = 120 900 7 = 128.6 1080 8 = 135 1260 9 = 140 1440 10 = 144 (n 2) x 180 n n 360 n (n 2) x 180

6. Answers 1800 1a. 1440 b. c. 1980 2a. 12 b. 20 c. 9 3. 154.3 4. 30 5. 3600 6. Wrong 7. 60 8a. 240 b. 120

7. Exam question ABCDEF is a regular hexagon. EFGH is a square. Angle DEH = x Work out the value of x. B C A D Ext angle of hex = 360 6 = 60 E F x Ext angle of square = 360 4 = 90 H G x = 90 + 60 = 150