Question

if m∠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 the equation

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: Combine like - terms

Combining the $x$ terms on the left - hand side gives $4x+2 = 90$.

Step3: Isolate the variable term

Subtract 2 from both sides: $4x=90 - 2=88$.

Step4: Solve for $x$

Divide both sides by 4: $x=\frac{88}{4}=22$.

Step5: Find the measure of $\angle B$

Substitute $x = 22$ into the expression for $m\angle B$: $m\angle B=3\times22 + 2=66 + 2=68^{\circ}$.

Step6: Find the measure of $\angle C$

Since $x = 22$, $m\angle C=22^{\circ}$.

Answer:

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