Question

1. if m∠p is three less than twice the measure of ∠q, and ∠p and ∠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, $m\angle P+m\angle Q = 180^{\circ}$, so $(2x - 3)+x=180$.

Step2: Simplify the equation

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

Step3: 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: $x=\frac{183}{3}=61$.

Step4: Find the measure of $\angle P$

Substitute $x = 61$ into the expression for $m\angle P$. $m\angle P=2x-3=2\times61 - 3=122 - 3=119^{\circ}$.

Answer:

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