Angles and Diagonals of a Regular Polygon

CAT 2023 Slot 3 · QA · Easy · Geometry

All CAT 2023 Slot 3 questionsMore Geometry questionsAll CAT QA

In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is

Answer

54

Explanation

Let II be the interior angle and EE be the exterior angle. We know I+E=180∘I + E = 180^\circ and I−E=120∘I - E = 120^\circ.

Subtracting gives: 2E=60∘  ⟹  E=30∘2E = 60^\circ \implies E = 30^\circ

Number of sides n=360∘E=360∘30∘=12n = \frac{360^\circ}{E} = \frac{360^\circ}{30^\circ} = 12.

Number of diagonals =n(n−3)2=12×92=54= \frac{n(n-3)}{2} = \frac{12 \times 9}{2} = 54.

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace