Question

in circle $v$, $m\angle stu = 50^\circ$. solve for $x$ if $m\overset{\frown}{su} = (10x - 23)^\circ$. 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 $m\angle STU = \frac{1}{2}m\overset{\frown}{SU}$.

Step2: Substitute given values

Substitute $m\angle STU=50^\circ$ and $m\overset{\frown}{SU}=(10x-23)^\circ$:
$50 = \frac{1}{2}(10x - 23)$

Step3: Multiply both sides by 2

Eliminate the fraction:
$50 \times 2 = 10x - 23$
$100 = 10x - 23$

Step4: Isolate the term with x

Add 23 to both sides:
$100 + 23 = 10x$
$123 = 10x$

Step5: Solve for x

Divide both sides by 10:
$x = \frac{123}{10} = 12.3$

Answer:

$12.3$