Question

Quadrilateral ABCD is inscribed in a circle. m∠A is 64°, m∠B is (6x + 4)°, and m∠C is (9x − 1)°. What is m∠D?

A. 64°
B. 82°
C. 90°
D. 98°
E. 116°

Answer 1

The answer is D. 98

A quadrilateral ABCD is cyclic if and only if its opposite angles are supplementary. A and C are opposite angles, so they are supplementary m∠A + m∠C = 180° 9x-1 + 64 = 180 9x+63 = 180 9x = 117 x = 13° m∠B = 6x+4 = 6(13)+4 = 82° B and D are opposite angles, so they are supplementary m∠B + m∠D = 180° 82° + m∠D = 180° m∠D = 98°