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 like - terms in the equation $(2x - 3)+x=180$, we get $2x+x-3 = 180$, which simplifies to $3x-3 = 180$.

Step3: Add 3 to both sides

Adding 3 to both sides of the equation $3x - 3=180$, we have $3x-3 + 3=180 + 3$, resulting in $3x=183$.

Step4: Solve for x

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

Step5: Find $m\angle P$ and $m\angle Q$

Since $x = m\angle Q=61^{\circ}$, and $m\angle P=2x - 3$, then $m\angle P=2\times61-3=122 - 3=119^{\circ}$.

Answer:

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