Question

in the figure below, m∠1 = 7x° and m∠2=(x + 2)°. find the angle measures.

Explanation:

Step1: Set up equation

Since $\angle1$ and $\angle2$ are complementary (sum to 90°), we have $7x+(x + 2)=90$.

Step2: Simplify left - hand side

Combining like terms, $7x+x+2=8x + 2$. So the equation becomes $8x+2 = 90$.

Step3: Solve for x

Subtract 2 from both sides: $8x=90 - 2=88$. Then divide both sides by 8, $x=\frac{88}{8}=11$.

Step4: Find measure of $\angle1$

Substitute $x = 11$ into the expression for $\angle1$. $m\angle1=7x=7\times11 = 77^{\circ}$.

Step5: Find measure of $\angle2$

Substitute $x = 11$ into the expression for $\angle2$. $m\angle2=x + 2=11+2=13^{\circ}$.

Answer:

$m\angle1 = 77^{\circ}$
$m\angle2 = 13^{\circ}$