Answer:
x = 4
Step-by-step explanation:
The measure of a chord- chord angle is half the sumof the measures of the arcs intercepted by the angle and its vertical angle
∠ UTV is a chord- chord angle , then
∠ UTV = [tex]\frac{1}{2}[/tex] ( UV + HW ) ← substitute values )
4 + 28x = [tex]\frac{1}{2}[/tex] ( 154 + 78)
4 + 28x = [tex]\frac{1}{2}[/tex] (232)
4 + 28x = 116 ( subtract 4 from both sides )
28x = 112 ( divide both sides by 28 )
x = 4
