Question

in the figure, m∠1=(x - 12)° and m∠2=(7x)°. (a) write an equation to find x. make sure you use an \=\ sign in your answer. equation: (b) find the degree measure of each angle. m∠1=° m∠2=°

Explanation:

Step1: Identify angle - relationship

Since $\angle1$ and $\angle2$ are supplementary (a straight - line forms an angle of 180°), we can write the equation.
$(x - 12)+7x=180$

Step2: Simplify the left - hand side of the equation

Combine like terms: $x+7x-12 = 180$, which gives $8x-12 = 180$.

Step3: Solve for x

Add 12 to both sides: $8x=180 + 12$, so $8x=192$. Then divide both sides by 8: $x=\frac{192}{8}=24$.

Step4: Find the measure of $\angle1$

Substitute $x = 24$ into the expression for $\angle1$: $m\angle1=(x - 12)=(24-12)=12^{\circ}$.

Step5: Find the measure of $\angle2$

Substitute $x = 24$ into the expression for $\angle2$: $m\angle2=7x=7\times24 = 168^{\circ}$.

Answer:

(a) Equation: $(x - 12)+7x=180$
(b) $m\angle1 = 12^{\circ}$
$m\angle2 = 168^{\circ}$