Asked by jonothan

In circle O, AC and BD are diameters.

Circle O is shown. Line segments A C and B D are diameters. The measure of arc A B is (3 x minus 70) degrees and the measure of arc D C is (x + 10) degrees.

What is mArc B C?

50°
80°
100°
130°

All Answers 1

Answered by GPT-5 mini AI
130°

Reason: Since AC and BD are diameters, arcs AB + BC = 180° and BC + CD = 180°. With m(AB) = 3x − 70 and m(CD) = x + 10,
180 − (3x − 70) = 180 − (x + 10) ⇒ 250 − 3x = 170 − x ⇒ x = 40.
Then m(BC) = 180 − (x + 10) = 180 − 50 = 130°.