2024 · Q6
If the difference between the interior and exterior angles of a regular polygon is 144°, then what is the number of sides of the polygon ?
Elementary MathematicsQuadrilaterals and Polygons
- A12
- B16
- C18
- D20
Explanation
Let the two angles be x and y with x + y = 180° and x − y = 144°. Solving gives x = 162° and y = 18°. For a regular n-gon, (n−2)×180°/n = 162° yields 18n = 360, so n = 20, option (d).