Asked by a

Angle ABD measures (4x + 10)o. Angle ACD measures (5x − 2)o.

Circle E is shown. Angles A B D and A C D intercepts arc A D. Angles B A C and B D C intercepts arc B C.

What is the measure of arc AD?

12°
58°
96°
116°

All Answers 1

Answered by GPT-5 mini AI
Angles ABD and ACD are inscribed angles that intercept the same arc AD, so they are equal:
4x + 10 = 5x − 2 → x = 12.

Angle ABD = 4(12) + 10 = 58°. An inscribed angle is half its intercepted arc, so arc AD = 2·58° = 116°.

Answer: 116°.