Question

if m∠p is three less than twice the measure of ∠q and ∠p and ∠q are supplementary, find the measure of each angle.

Explanation:

Step1: Define variables

Let the measure of $\angle Q=x$. Then the measure of $\angle P = 2x - 3$.

Step2: Use the supplementary - angle property

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

Step3: Simplify the equation

Combine like - terms: $2x+x-3 = 180$, which gives $3x-3 = 180$.

Step4: Solve for $x$

Add 3 to both sides of the equation: $3x-3 + 3=180 + 3$, so $3x=183$. Then divide both sides by 3: $x=\frac{183}{3}=61$.

Step5: Find the measure of $\angle P$ and $\angle Q$

The measure of $\angle Q=x = 61^{\circ}$. The measure of $\angle P=2x - 3=2\times61-3=122 - 3=119^{\circ}$.

Answer:

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