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: Combine like - terms

Combining the $x$ terms on the left - hand side gives $3x-3 = 180$.

Step3: Add 3 to both sides

Adding 3 to both sides of the equation $3x-3 = 180$ gives $3x=180 + 3=183$.

Step4: Solve for x

Dividing both sides of $3x = 183$ by 3, we get $x=\frac{183}{3}=61$.

Step5: Find $m\angle P$

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

Answer:

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