Question

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

Answer 1

Answer:

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

Step-by-step 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°}