PrepRung
Sign inSign up free

CAT 2017 Slot 2 · Quant · Polygons and Quadrilaterals · medium

Each interior angle of a regular polygon is 150°. How many diagonals does the polygon have?

Single correct option

Each interior angle of a regular polygon is 150°. How many diagonals does the polygon have?
  1. A. 44
  2. B. 54
  3. C. 65
  4. D. 77
Show answer and solution

Answer: (B) 54

Each exterior angle = 180° − 150° = 30°, and the exterior angles sum to 360°, so n = 360/30 = 12.

Number of diagonals = n(n − 3)/2 = 12 × 9/2 = 54.

(44, 65 and 77 are the diagonal counts for 11-, 13- and 14-gons.)
Report a mistake

Original question written in the CAT 2017 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake