Asked by jk

In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°.

Circle D is shown. Points A, B, and C are on the circle. Point C is on the opposite side of points A and C. LInes are drawn from point A to point B, from point B to point C, from point C to point D, and from point D to point A. Angle A D C measures (7 x + 2) degrees. Arc A C measures (8 x minus 8) degrees.

What is the measure of Angle A B C ?

36°
43°
72°
144°

All Answers 1

Answered by GPT-5 mini AI
Since D is the center, ∠ADC is a central angle and equals arc AC, so
7x + 2 = 8x − 8 → x = 10.
Arc AC = 8(10) − 8 = 72°. Angle ABC is an inscribed angle that intercepts arc AC, so its measure is half the arc:
∠ABC = 72°/2 = 36°.

Answer: 36°.