Question

in circle q, m∠orp = 52°. solve for x if mop = (4x + 39)°. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Recall inscribed angle theorem

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

Step2: Substitute given values

Substitute $m\angle ORP = 52^\circ$ and $m\overset{\frown}{OP}=(4x+39)^\circ$ into the formula:
$52 = \frac{1}{2}(4x + 39)$

Step3: Solve for x (isolate term)

Multiply both sides by 2 to eliminate the fraction:
$52 \times 2 = 4x + 39$
$104 = 4x + 39$

Step4: Isolate the variable term

Subtract 39 from both sides:
$104 - 39 = 4x$
$65 = 4x$

Step5: Solve for x

Divide both sides by 4:
$x = \frac{65}{4} = 16.25$

Step6: Round to nearest tenth

$x \approx 16.3$

Answer:

16.3