Question

in the figure below, m∠1 = (x + 6)° and m∠2 = 6x°. find the angle measures.

Explanation:

Step1: Set up equation

Since $\angle1$ and $\angle2$ are complementary (sum to 90°), we have $(x + 6)+6x=90$.

Step2: Combine like - terms

Combining $x$ terms gives $7x+6 = 90$.

Step3: Isolate $x$

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

Step4: Find $\angle1$ measure

Substitute $x = 12$ into the expression for $\angle1$: $m\angle1=(x + 6)=(12+6)=18^{\circ}$.

Step5: Find $\angle2$ measure

Substitute $x = 12$ into the expression for $\angle2$: $m\angle2=6x=6\times12 = 72^{\circ}$.

Answer:

$m\angle1 = 18^{\circ}$
$m\angle2 = 72^{\circ}$