Question

Find the measurement of one interior angle in each polygon. Round your answers to the nearest tenth if necessary.

Find the measure of one exterior angle in each polygon. Round your answer to the nearest tenth if necessary.

Answer 1

1. 108°
2. 120°
3. 147.3°
4. 90°
5. 72°
6. 40°
7. 51.4°
8. 90°

Explanation:

1–4: The interior angle of an n-sided regular polygon is (n-2)/n times 180°. For n ∈ {5, 6, 11, 4}, this is {3/5, 4/6, 9/11, 2/4} · 180°, or {108°, 120°, 147.3°, 90°}

5–8: The exterior angle of an n-sided regular polygon is 360°/n. For n ∈ {5, 9, 7, 4}, this is 360°/{5, 9, 7, 4}, or {72°, 40°, 51.4°, 90°}