Question

in the figure, m∠1=(x - 12)° and m∠2=(5x)°. (a) write an equation to find x. make sure you use an \=\ sign in your answer. (b) find the degree measure of each angle. m∠1=° m∠2=°

Explanation:

Step1: Assume angles are supplementary

If $\angle1$ and $\angle2$ are supplementary (sum to 180°), we set up the equation.
$x - 12+5x=180$

Step2: Combine like - terms

Combine the $x$ terms on the left - hand side.
$6x-12 = 180$

Step3: Add 12 to both sides

Isolate the term with $x$.
$6x=180 + 12$
$6x=192$

Step4: Solve for $x$

Divide both sides by 6.
$x=\frac{192}{6}=32$

Step5: Find $m\angle1$

Substitute $x = 32$ into the expression for $m\angle1$.
$m\angle1=x - 12=32-12 = 20$

Step6: Find $m\angle2$

Substitute $x = 32$ into the expression for $m\angle2$.
$m\angle2=5x=5\times32 = 160$

Answer:

(a) Equation: $x - 12+5x=180$
(b) $m\angle1 = 20^{\circ}$
$m\angle2 = 160^{\circ}$