Question

1. if ( m angle 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 the equation

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

Step2: Solve the equation

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

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

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

Answer:

The measure of \(\angle P\) is \(119^{\circ}\) and the measure of \(\angle Q\) is \(61^{\circ}\).