If the interior angle of a regular polygon is k times its exterior angle, express the number of sides n of the polygon in terms of k.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 2k + 2.
Interior angle = k × exterior angle
Interior angle = [(n – 2) × 180]/n
Exterior angle = 360/n
[(n – 2) × 180]/n = k × 360/n
⇒ (n–2) × 180 = k × 360
⇒ n – 2 = 2k
⇒ n = 2k + 2