Question

1. if ∠b is two more than three times the measure of ∠c, and ∠b and ∠c are complementary angles, find each angle measure.

Explanation:

Step1: Set up equations

Let $m\angle C=x$. Then $m\angle B = 3x + 2$. Since $\angle B$ and $\angle C$ are complementary, $m\angle B+m\angle C=90^{\circ}$. So, $(3x + 2)+x=90$.

Step2: Simplify the equation

Combine like - terms: $3x+x+2 = 90$, which gives $4x+2=90$.

Step3: Solve for $x$

Subtract 2 from both sides: $4x=90 - 2=88$. Then divide both sides by 4: $x=\frac{88}{4}=22$.

Step4: Find the measure of each angle

$m\angle C=x = 22^{\circ}$. $m\angle B=3x + 2=3\times22+2=66 + 2=68^{\circ}$.

Answer:

$m\angle B = 68^{\circ}$, $m\angle C=22^{\circ}$