Question

In a cyclic quadrilateral ABCD, twice the measure of ∠A is thrice the measure of ∠C. Find the measure of ∠C? 

(A) 36° 

(B) 72° 

(C) 90° 

(D) 108°

Answer 1

(B) 72°

∠A + ∠C = 180° [Theorem of cyclic quadrilateral] 

∴ 2∠A + 2∠C = 2 × 180° [Multiplying both sides by 2] 

∴ 3∠C + 2∠C = 360° [∵ 2∠A = 3∠C] 

∴ 5∠C = 360° 

∴ ∠C = 72°