In circle TT, m, angle, U, T, V, equals, 64, degreesm∠UTV=64
∘
. Solve for xx if m, arc, U, V, equals, left bracket, 4, x, plus, 43, right bracket, degreesm
UV
⌢
=(4x+43)
∘
. If necessary, round your answer to the nearest tenth.
To solve for x, we first need to use the formula relating the measure of an inscribed angle to the measure of the arc it intercepts:
m∠UTV = 1/2 * m arc UV
Substitute in the given values:
64 = 1/2 * (4x + 43)
64 = 2x + 43
2x = 21
x = 10.5
Therefore, x is approximately 10.5.