Question

in the figure below, m∠1=(x + 18)° and m∠2 = 5x°. find the angle measures.

Explanation:

Step1: Set up equation

Since $\angle1$ and $\angle2$ are complementary (assuming they form a right - angle as they seem to be parts of a 90 - degree angle), we have $(x + 18)+5x=90$.

Step2: Combine like terms

Combining the $x$ terms on the left - hand side gives $6x+18 = 90$.

Step3: Isolate the variable term

Subtract 18 from both sides: $6x=90 - 18$, so $6x=72$.

Step4: Solve for $x$

Divide both sides by 6: $x=\frac{72}{6}=12$.

Step5: Find $m\angle1$

Substitute $x = 12$ into the expression for $\angle1$: $m\angle1=x + 18=12+18 = 30^{\circ}$.

Step6: Find $m\angle2$

Substitute $x = 12$ into the expression for $\angle2$: $m\angle2=5x=5\times12 = 60^{\circ}$.

Answer:

$m\angle1 = 30^{\circ}$
$m\angle2 = 60^{\circ}$