Question

1. ray sq bisects ∠rst and the measure of ∠rsq = 4x - 8. if ∠rst = 80, what is the value of x?

a. 12
b. 22
c. 80
d. 40

Explanation:

Step1: Use the angle - bisector property

Since ray \(SQ\) bisects \(\angle RST\), then \(\angle RSQ=\frac{1}{2}\angle RST\).
Given \(\angle RST = 80\), so \(\angle RSQ=\frac{80}{2}=40\).

Step2: Set up the equation

We know that \(\angle RSQ = 4x−8\), and \(\angle RSQ = 40\). Then the equation is \(4x−8 = 40\).

Step3: Solve the equation for \(x\)

Add \(8\) to both sides of the equation: \(4x-8 + 8=40 + 8\), which simplifies to \(4x=48\).
Divide both sides by \(4\): \(x=\frac{48}{4}=12\).

Answer:

A. 12