Question

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

Answer 1

25.0

Explanation:

just took quiz and got it right

Answer 2

x = 25.0

Explanation:

If ST is a diameter, then m∠TOS = 180°.

From the picture we have the equation:

m∠TOU + m∠UOR + m∠ROS = m∠TOS We have:

m∠TOU = (3x - 14)°

m∠UOR = (3x - 14)°

m∠ROS = (2x + 8)°

m∠TOS = 180°

Substitute:

(3x - 14) + (3x - 14) + (2x + 8) = 180 combine like terms

(3x + 3x + 2x) + (-14 - 14 + 8) = 180

8x - 20 = 180 add 20 to both sides

8x - 20 + 20 = 180 + 20

8x = 200 divide both sides by 8

8x/8 = 200/8

x = 25