Question

in the figure, (mangle1=(x + 66)^{circ}) and (mangle2=(2x)^{circ}). (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. (mangle1=) (^{circ}) (mangle2=) (^{circ})

Explanation:

Step1: Use angle - addition property

Since $\angle1$ and $\angle2$ are supplementary (form a straight - line), their sum is $180^{\circ}$. So, $(x + 66)+2x=180$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side gives $3x+66 = 180$.

Step3: Isolate the variable term

Subtract 66 from both sides: $3x=180 - 66$, so $3x=114$.

Step4: Solve for $x$

Divide both sides by 3: $x=\frac{114}{3}=38$.

Step5: Find $m\angle1$

Substitute $x = 38$ into the expression for $m\angle1$: $m\angle1=x + 66=38+66 = 104^{\circ}$.

Step6: Find $m\angle2$

Substitute $x = 38$ into the expression for $m\angle2$: $m\angle2=2x=2\times38 = 76^{\circ}$.

Answer:

(a) Equation: $(x + 66)+2x=180$
(b)
$m\angle1 = 104^{\circ}$
$m\angle2 = 76^{\circ}$