1. The Interior Angles of Polygons

2. Sum of the interior angles in a polygon We’ve seen that a quadrilateral can be divided into two triangles … … and a pentagon can be divided into three triangles. How many triangles can a hexagon be divided into? A hexagon can be divided into four triangles.

3. Sum of the interior angles in a polygon The number of triangles that a polygon can be divided into is always two less than the number of sides. We can say that: A polygon with n sides can be divided into ( n – 2) triangles. The sum of the interior angles in a triangle is 180°. So: The sum of the interior angles in an n -sided polygon is ( n – 2) × 180°.

4. Interior angles in regular polygons A regular polygon has equal sides and equal angles. We can work out the size of the interior angles in a regular polygon as follows: Name of regular polygon Sum of the interior angles Size of each interior angle Equilateral triangle180°180° ÷ 3 =60° Square2 × 180° = 360°360° ÷ 4 =90° Regular pentagon3 × 180° = 540°540° ÷ 5 =108° Regular hexagon4 × 180° = 720°720° ÷ 6 =120°

5. Interior angles in regular polygons A regular polygon has equal sides and equal angles. We can work out the size of the interior angles in a regular polygon as follows: Name of regular polygon Sum of the interior angles Size of each interior angle Equilateral triangle180°180° ÷ 3 =60° Square2 × 180° = 360°360° ÷ 4 =90° Regular pentagon3 × 180° = 540°540° ÷ 5 =108° Regular hexagon4 × 180° = 720°720° ÷ 6 =120°

6. Now try these: 1.Use the formula to find the sum of the angles of a polygon with: a. 11 sides b. 14 sides c. 19 sides d. 23 sides e. 47 sides f. 120 sides g. 152 sides 2. Use the inverse of the formula to find the number of sides of polygon whose internal angles total: a.1980°b. 2700° c. 3600° d. 9180° e. 4680° f. 7920° g. 4860°

7. Answers: 1a. 1620b. 2160c. 3060d. 3780 e. 8100f. 21’240g. 27’000 2a. 13b. 17c. 22d. 53 e. 28f. 46g. 29