Question

in circle $u$, $m\angle svt = 73^\circ$. solve for $x$ if $m\overset{\frown}{st} = (6x - 20)^\circ$. 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 $m\angle SVT = \frac{1}{2}m\overset{\frown}{ST}$.
Substitute the given values: $73 = \frac{1}{2}(6x - 20)$

Step2: Multiply both sides by 2

Eliminate the fraction to simplify the equation.
$73 \times 2 = 6x - 20$
$146 = 6x - 20$

Step3: Isolate the term with $x$

Add 20 to both sides of the equation.
$146 + 20 = 6x$
$166 = 6x$

Step4: Solve for $x$

Divide both sides by 6 and round to the nearest tenth.
$x = \frac{166}{6} \approx 27.7$

Answer:

$x \approx 27.7$