Question

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

Explanation:

Step1: Recall 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

$$3x + 22 = 59$$

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:
$$x = \frac{37}{3} \approx 17.3$$

Answer:

$x = 17.3$