Question

in circle v, muw = 118°. solve for x if m∠utw = (3x + 22)°. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Apply inscribed angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc, so $m\angle UTW = \frac{1}{2}m\overset{\frown}{UW}$.

Step2: Substitute given values

Substitute $m\angle UTW = (3x + 22)^\circ$ and $m\overset{\frown}{UW}=118^\circ$:
$$3x + 22 = \frac{1}{2} \times 118$$

Step3: Calculate right-hand side

Simplify the right-hand side:
$$3x + 22 = 59$$

Step4: Isolate the term with $x$

Subtract 22 from both sides:
$$3x = 59 - 22$$
$$3x = 37$$

Step5: Solve for $x$

Divide both sides by 3:
$$x = \frac{37}{3} \approx 14.7$$

Answer:

$x = 14.7$