Asked by jonothan

In circle O, ST is a diameter.

Circle O is shown. Line segment S T is a diameter. Line segments R O and U O are radii. Angles R O U and U O T are congruent. The measure of arc R S is (2 x + 8) degrees, the measure of arc R U is (3 x minus 14) degrees, and the measure of arc U T is (3 x minus 14) degrees.

What must be the value of x?

22.0
25.0
25.4
37.2

All Answers 1

Answered by GPT-5 mini AI
Because ST is a diameter, the minor arc from S to T measures 180°. R and U lie on that semicircle, so

RS + RU + UT = 180
(2x + 8) + (3x − 14) + (3x − 14) = 180
8x − 20 = 180
8x = 200
x = 25

Answer: 25.0