Question

applying the second corollary to the inscribed angles theorem
the measure of arc qs is $(4x - 18)^{circ}$.
what is the value of $x$
○ 40.5
○ 49.5
○ 94.5
○ 180

Explanation:

Step1: Identify arc measure rule

An inscribed angle that intercepts a semicircle is a right angle ($90^\circ$), so the intercepted arc QS is a semicircle with measure $180^\circ$.

Step2: Set up equation for arc QS

Set the given arc measure equal to $180^\circ$:
$4x - 18 = 180$

Step3: Solve for x

Add 18 to both sides:
$4x = 180 + 18 = 198$
Divide by 4:
$x = \frac{198}{4} = 49.5$

Answer:

49.5