Question

1. the measure of ∠p is five less than four times the measure of ∠q. if ∠p and ∠q are supplementary angles, find m∠p.

Explanation:

Step1: Set up equations

Let $m\angle P=x$ and $m\angle Q = y$. We know that $x = 4y- 5$ (given relationship between angles) and $x + y=180$ (since they are supplementary).

Step2: Substitute

Substitute $x = 4y - 5$ into $x + y=180$. We get $(4y-5)+y = 180$.

Step3: Simplify the equation

Combine like - terms: $4y+y-5=180$, which simplifies to $5y-5 = 180$.

Step4: Solve for $y$

Add 5 to both sides: $5y=180 + 5=185$. Then divide both sides by 5, so $y=\frac{185}{5}=37$.

Step5: Solve for $x$

Substitute $y = 37$ into $x = 4y-5$. Then $x=4\times37-5=148 - 5=143$.

Answer:

$m\angle P = 143^{\circ}$