Question

applying the second corollary to the inscribed angles theorem
the measure of arc qs is (4x - 18)°.
what is the value of x?
94.5
49.5
180

Explanation:

Step1: Use the second corollary to the inscribed angles theorem

The second corollary to the inscribed angles theorem states that an angle inscribed in a semicircle is a right angle. Here, \(\angle R = 90^{\circ}\), so arc \(QS\) is a semicircle. The measure of a semicircle is \(180^{\circ}\).

Step2: Set up the equation

We know that the measure of arc \(QS=(4x - 18)^{\circ}\), and since it is a semicircle, \(4x-18 = 180\).

Step3: Solve the equation for \(x\)

Add \(18\) to both sides of the equation: \(4x=180 + 18\), so \(4x=198\).
Divide both sides by \(4\): \(x=\frac{198}{4}=49.5\).

Answer:

\(49.5\)