Each interior angle of a regular polygon exceeds its exterior angle by 150°. Determine the number of sides of the polygon.
Show answer & explanation
Correct answer: D
Explanation
Interior angle = Exterior angle + 150°
Interior + Exterior = 180°
Exterior = 360°/n
Let the exterior angle be x, and the interior angle be x + 150.
⇒ x + (x + 150) = 180
⇒ 2x + 150 = 180
⇒ 2x = 30
⇒ x = 15°
360/n = 15
n = 360/15
n = 24 sides