Question

circle s, m∠utv = 51°. solve for x if muv = (5x + 23)°. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Apply inscribed angle theorem

$m\angle UTV = \frac{1}{2}m\overset{\frown}{UV}$

Step2: Substitute given values

$51 = \frac{1}{2}(5x + 23)$

Step3: Multiply both sides by 2

$102 = 5x + 23$

Step4: Isolate the term with $x$

$5x = 102 - 23 = 79$

Step5: Solve for $x$

$x = \frac{79}{5} = 15.8$

Answer:

$x=15.8$