1. 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

2. 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

3. 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

4. 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

5. 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