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?22.025.025.437.2
Accepted Solution
A:
Answer:x = 25.0Step-by-step 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) = 1808x - 20 = 180 add 20 to both sides8x - 20 + 20 = 180 + 208x = 200 divide both sides by 88x/8 = 200/8x = 25