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: (b) find the degree measure of each angle. m∠1= ° m∠2= °

Explanation:

Step1: Note angle - relationship

Since $\angle1$ and $\angle2$ are supplementary (linear - pair of angles), their sum is $180^{\circ}$. So the equation is $5x+(x - 18)=180$.

Step2: Simplify the equation

Combine like - terms: $5x+x-18 = 180$, which gives $6x-18 = 180$.

Step3: Isolate the variable term

Add 18 to both sides of the equation: $6x-18 + 18=180 + 18$, so $6x=198$.

Step4: Solve for x

Divide both sides by 6: $x=\frac{198}{6}=33$.

Step5: Find the measure of $\angle1$

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

Step6: Find the measure of $\angle2$

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

Answer:

(a) Equation: $5x+(x - 18)=180$
(b) $m\angle1 = 165^{\circ}$
$m\angle2 = 15^{\circ}$