Question

1. points p, q, and s are collinear. what is m∠pqr?

a. 132
b. 130
c. 138
d. 126

Explanation:

Step1: Use the property of collinear points

Since points \(P\), \(Q\), and \(S\) are collinear, \(\angle PQR+\angle RQS = 180^{\circ}\). So, \((3x - 6)+(x + 2)=180\).

Step2: Solve the equation for \(x\)

Combine like - terms: \(3x+x-6 + 2=180\), which simplifies to \(4x-4 = 180\).
Add \(4\) to both sides: \(4x=180 + 4=184\).
Divide both sides by \(4\): \(x=\frac{184}{4}=46\).

Step3: Find the measure of \(\angle PQR\)

Substitute \(x = 46\) into the expression for \(\angle PQR\) (\(3x-6\)).
\(3x-6=3\times46-6\).
First, calculate \(3\times46 = 138\), then \(138-6=132\).

Answer:

A. 132