Question

what is the value of x?

x = o

Explanation:

Step1: Use the inscribed - angle theorem

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc.
The central angle $\angle SQR = 82^{\circ}$, and the inscribed angle $\angle STR=2x + 17^{\circ}$.
So, $2x+17=\frac{1}{2}\times82$.

Step2: Solve the equation for $x$

First, simplify the right - hand side of the equation: $\frac{1}{2}\times82 = 41$.
The equation becomes $2x+17 = 41$.
Subtract 17 from both sides: $2x=41 - 17$.
$2x=24$.
Divide both sides by 2: $x=\frac{24}{2}$.

Answer:

$x = 12$