Question

1. if ( mangle p ) is three less than twice the measure of ( angle q ), and ( angle p ) and ( angle q ) are supplementary angles, find each angle measure.

Explanation:

Step1: Set up equations

Let \(m\angle Q = x\). Then \(m\angle P=2x - 3\). Since \(\angle P\) and \(\angle Q\) are supplementary, \(m\angle P+m\angle Q = 180^{\circ}\). Substitute the expressions: \((2x - 3)+x=180\).

Step2: Solve for \(x\)

Combine like terms: \(2x+x-3 = 180\), so \(3x-3 = 180\). Add 3 to both sides: \(3x=180 + 3=183\). Divide by 3: \(x=\frac{183}{3}=61\).

Step3: Find \(m\angle P\)

Substitute \(x = 61\) into \(m\angle P=2x - 3\). Then \(m\angle P=2\times61-3=122 - 3=119\).

Answer:

\(m\angle Q = 61^{\circ}\), \(m\angle P=119^{\circ}\)