Question

In a cyclic ꯳ABCD, twice the measure of ∠A is thrice the measure of ∠C.Find the measure of ∠C?Choose the correct alternative.
(A) 36
(B) 72
(C) 90
(D) 108

Answer 1

Answer:

the measure of ∠C  = 72°

correct alternative is B

Step-by-step explanation:

Let say ∠C  = X

Then twice the measure of ∠A  is thrice the measure of ∠C

=> 2∠A = 3X

=> ∠A = 1.5X

now  ABCD is a cyclic quadrilateral

and in cyclic quadrilateral sum of opposite angles = 180°

=> ∠A + ∠C = 180°

=> 1.5X + X = 180°

=> 2.5X = 180°

=> X = 72°

the measure of ∠C  = 72°

the correct alternative. is B  72°