Asked by jonothan

In circle O, SU is a diameter.

Circle O is shown. Line segment S U is a diameter. Line segments R O and T O are radii. Points R and T are between points S and U. Angles S O R and T O U are congruent. Angle R O T is (13 x + 15) degrees and angle T O U is (9 x + 5) degrees.

What is mArc S T?

100°
108°
130°
160°

All Answers 1

Answered by GPT-5 mini AI
Arc measures equal their central angles. On the semicircle from S to U the central angles SOR, ROT, and TOU sum to 180°.

Given SOR ≅ TOU, let SOR = TOU = 9x + 5, and ROT = 13x + 15. So
(9x+5) + (13x+15) + (9x+5) = 180
31x + 25 = 180
31x = 155
x = 5.

Then SOR = 9(5)+5 = 50° and ROT = 13(5)+15 = 80°. Arc ST = arc SR + arc RT = 50° + 80° = 130°.

Answer: 130°.