Angles and Polygons COURSE 3 LESSON 8-6

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Presentation transcript:

Angles and Polygons COURSE 3 LESSON 8-6 Find the sum of the measures of the interior angles of an octagon. An octagon has 8 sides. (n – 2) 180º = (8 – 2) 180º Substitute 8 for n. = 1,080º Simplify. 8-6

Angles and Polygons Find the missing angle measure in the hexagon. COURSE 3 LESSON 8-6 Find the missing angle measure in the hexagon. Step 1 Find the sum of the measures of the interior angles of a hexagon. (n – 2) 180° = (6 – 2) 180° Substitute 6 for n. Simplify. = 720° 8-6

Angles and Polygons Step 2 Write an equation. COURSE 3 LESSON 8-6 (continued) Step 2 Write an equation. Let x = the missing angle measure. 720° = 120° + 115° + 136° + 80° + 147° + x° Write an equation. 720° = 598° + x° Add. 122° = x° Subtract 598º from each side. The missing angle measure is 122º. 8-6

COURSE 3 LESSON 8-6 Angles and Polygons A design on a tile is in the shape of a regular nonagon. Find the measure of each angle. Find the sum of the measures of the interior angles of the nonagon. (n – 2) 180° = (9 – 2) 180° Substitute 9 for n. = 1,260° Simplify. 1,260° ÷ 9 = 140° Divide the sum by the number of angles. Each angle of a regular nonagon has a measure of 140°. 8-6

COURSE 3 LESSON 8-6 Angles and Polygons 1. Find the sum of the measures of the interior angles of a polygon having 17 sides. 2. Five angles of a hexagon measure 128°, 190°, 112°, 154°, and 90°. Find the measure of the missing angle. 3. Find the measure of each angle of a regular polygon having 24 sides. 2,700° 46° 165° 8-6