Question

in the figure, m∠1=(x - 4)° 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 is 180°), we have the equation $(x - 4)+7x=180$.

Step2: Simplify the left - hand side

Combine like terms: $x-4 + 7x=(x + 7x)-4=8x-4$. So the equation becomes $8x-4 = 180$.

Step3: Solve for x

Add 4 to both sides of the equation: $8x-4 + 4=180 + 4$, which gives $8x=184$. Then divide both sides by 8: $x=\frac{184}{8}=23$.

Step4: Find the measure of $\angle1$

Substitute $x = 23$ into the expression for $m\angle1$: $m\angle1=(x - 4)=(23-4)=19^{\circ}$.

Step5: Find the measure of $\angle2$

Substitute $x = 23$ into the expression for $m\angle2$: $m\angle2=(7x)=7\times23 = 161^{\circ}$.

Answer:

(a) Equation: $(x - 4)+7x=180$
(b) $m\angle1 = 19^{\circ}$
$m\angle2 = 161^{\circ}$