EXAMPLE 1 Find the sum of angle measures in a polygon Find the sum of the measures of the interior angles of a convex octagon. SOLUTION An octagon has 8 sides. Use the Polygon Interior Angles Theorem. (n – 2) 180° = Substitute 8 for n. (8 – 2) 180° Subtract. = 6 180° Multiply. = 1080° ANSWER The sum of the measures of the interior angles of an octagon is 1080°.

EXAMPLE 2 Find the number of sides of a polygon The sum of the measures of the interior angles of a convex polygon is 900°. Classify the polygon by the number of sides. SOLUTION Use the Polygon Interior Angles Theorem to write an equation involving the number of sides n. Then solve the equation to find the number of sides. Polygon Interior Angles Theorem (n –2) 180° = 900° Divide each side by 180°. n –2 =5 Add 2 to each side. n = 7 The polygon has 7 sides. It is a heptagon. ANSWER

GUIDED PRACTICE for Examples 1 and 2 The coin shown is in the shape of a regular 11- gon. Find the sum of the measures of the interior angles. 1. SOLUTION Use the polygon Interior Angles Theorem (n – 2) 180 = Substitute 11 for n. (11 – 2) 180 Subtract. = Multiply. = 1620° ANSWER The sum of the measures of the interior angles is 1620°.

GUIDED PRACTICE for Examples 1 and 2 The sum of the measures of the interior angles of a convex polygon is 1440°. Classify the polygon by the number of sides. 2. SOLUTION Polygon Interior Angles Theorem (n – 2) 180 = 1440 Divide each side by 180°. Add 2 to each side. n =10 ANSWER The polygon has 10 sides. It is a decagon. 8 (n – 2) =