Question

applying the second corollary to the inscribed angles theorem. the measure of arc qs is (4x - 18)°. what is the value of x? 40.5 49.5 94.5 180

Explanation:

Step1: Recall the inscribed - angle theorem corollary

An angle inscribed in a semi - circle is a right angle. The arc that subtends a right - inscribed angle is a semi - circle, and the measure of a semi - circle is 180°. So, the measure of arc QS is 180°.

Step2: Set up the equation

We know that the measure of arc QS is (4x - 18)°. Set up the equation 4x−18 = 180.

Step3: Solve the equation for x

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

Answer:

49.5