Question

question
examples
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.
answer
attempt 1 out of 2
$x = $

Explanation:

Step1: Recall inscribed angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. So $\text{m}\angle STU = \frac{1}{2} \text{m}\overset{\frown}{SU}$

Step2: Substitute given values

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

Step3: Multiply both sides by 2

Eliminate the fraction by multiplying both sides by 2:
$50 \times 2 = 10x - 23$
$100 = 10x - 23$

Step4: Isolate the variable term

Add 23 to both sides to isolate the term with $x$:
$100 + 23 = 10x$
$123 = 10x$

Step5: Solve for x

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

Answer:

$x = 12.3$