Question

for two complementary angles, m∠a=(7x - 12)° and m∠b=(5x + 18)°. solve for x, then find m∠a. x = 15, m∠a = 93

Explanation:

Step1: Recall complementary - angle property

Since $\angle A$ and $\angle B$ are complementary, $m\angle A + m\angle B=90^{\circ}$. So, $(7x - 12)+(5x + 18)=90$.

Step2: Simplify the left - hand side

Combine like terms: $7x+5x-12 + 18=12x + 6$. So, the equation becomes $12x+6 = 90$.

Step3: Solve for x

Subtract 6 from both sides: $12x=90 - 6=84$. Then divide both sides by 12: $x=\frac{84}{12}=7$.

Step4: Find $m\angle A$

Substitute $x = 7$ into the expression for $m\angle A$: $m\angle A=7x-12=7\times7-12=49 - 12=37^{\circ}$.

Answer:

$x = 7$, $m\angle A=37^{\circ}$