Question

10 fill in the blank 2 points if m∠b is two more than three times the measure of ∠c, and ∠b and ∠c are complementary angles, find each angle measure. m∠b = type your answer... ° m∠c = type your answer... °

Explanation:

Step1: Set up equations

Let $m\angle C = x$. Then $m\angle B=3x + 2$. Since $\angle B$ and $\angle C$ are complementary, $m\angle B+m\angle C = 90$. 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 $m\angle B$ and $m\angle C$

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

Answer:

$m\angle B = 68$
$m\angle C = 22$