2024 · Q95
The ratio of sum of interior angles to sum of exterior angles of a regular polygon of n sides is 7/2. What is the measure of an interior angle of polygon?
Elementary MathematicsQuadrilaterals and Polygons
- A110°
- B120°
- C130°
- D140°
Explanation
Sum of interior angles = (n−2)×180° and sum of exterior angles = 360°. The ratio (n−2)×180/360 = 7/2 simplifies to (n−2)/2 = 7/2, giving n = 9. Each interior angle of the regular nonagon is (9−2)×180/9 = 140° — option D.