Question

in the figure, m∠1=(5x)° and m∠2=(x - 18)°. (a) write an equation to find x. make sure you use an \=\ sign in your answer equation: 5x + x - 18 = 180 (b) find the degree measure of each angle. m∠1=° m∠2=°

Explanation:

Step1: Combine like - terms in the equation

Combine $5x$ and $x$ in the equation $5x + x-18 = 180$. We get $6x-18 = 180$.
$5x+x-18=180\Rightarrow6x - 18=180$

Step2: Add 18 to both sides

To isolate the term with $x$, add 18 to both sides of the equation $6x - 18=180$.
$6x-18 + 18=180 + 18\Rightarrow6x=198$

Step3: Solve for x

Divide both sides of the equation $6x = 198$ by 6.
$x=\frac{198}{6}=33$

Step4: Find the measure of $\angle1$

Substitute $x = 33$ into the expression for $m\angle1=(5x)^{\circ}$.
$m\angle1=5\times33^{\circ}=165^{\circ}$

Step5: Find the measure of $\angle2$

Substitute $x = 33$ into the expression for $m\angle2=(x - 18)^{\circ}$.
$m\angle2=(33 - 18)^{\circ}=15^{\circ}$

Answer:

$m\angle1 = 165^{\circ}$
$m\angle2 = 15^{\circ}$