Question

in the figure, m∠1=(5x)° and m∠2=(x - 24)°. (a) write an equation to find x. make sure you use an \=\ sign in your answer. equation: 5x + x - 24 = 80 (b) find the degree measure of each angle. m∠1 = 170° m∠2 = 10°

Explanation:

Step1: Combine like - terms

Combine the $x$ terms in the equation $5x + x-24 = 180$ (assuming the two angles are supplementary, since the sum of adjacent angles on a straight - line is 180 degrees, the 80 in the original equation seems to be a mistake). We get $(5 + 1)x-24=180$, which simplifies to $6x-24 = 180$.

Step2: Add 24 to both sides

To isolate the term with $x$, we add 24 to both sides of the equation. So, $6x-24 + 24=180 + 24$, which gives $6x=204$.

Step3: Solve for $x$

Divide both sides of the equation $6x = 204$ by 6. We have $x=\frac{204}{6}=34$.

Step4: Find $m\angle1$

Substitute $x = 34$ into the expression for $m\angle1$. Since $m\angle1=(5x)^{\circ}$, then $m\angle1 = 5\times34=170^{\circ}$.

Step5: Find $m\angle2$

Substitute $x = 34$ into the expression for $m\angle2$. Since $m\angle2=(x - 24)^{\circ}$, then $m\angle2=34 - 24 = 10^{\circ}$.

Answer:

(a) Equation: $5x+x - 24=180$
(b) $m\angle1 = 170^{\circ}$
$m\angle2 = 10^{\circ}$