CAT 2019 Geometry & Mensuration Question (Hard)

Question

Let A and B be two regular polygons having a and b sides, respectively. If b 2a and each interior angle of B is 3 2 times each interior angle of A, then each interior angle, in degrees, of a regular polygon with a b sides is

Accepted Answer

Step 1 We are given - - Interior angle of B interior angle of A. Recall Interior angle of regular polygon with sides theta_n n Thus theta_b 2 theta_a Substitute formula b 2 times a cancels out b 2 times a Now cross-multiply 2 b-2 a 3b a -2 Since Substitute Simplify First term Second term Thus Simpli

CAT 2019

Quantitative

Geometry & Mensuration

Hard

Let A and B be two regular polygons having a and b sides, respectively. If b = 2a and each interior angle of B is 3/2 times each interior angle of A, then each interior angle, in degrees, of a regular polygon with a + b sides is

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