Question

in the figure, (mangle1=(x + 32)^{circ}) and (mangle2=(3x)^{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: Set up the equation

Since $\angle1$ and $\angle2$ are supplementary (a straight - line is 180°), we have $(x + 32)+3x=180$.

Step2: Combine like terms

Combining the $x$ terms on the left - hand side gives $4x+32 = 180$.

Step3: Isolate the variable term

Subtract 32 from both sides: $4x=180 - 32$, so $4x=148$.

Step4: Solve for x

Divide both sides by 4: $x=\frac{148}{4}=37$.

Step5: Find the measure of $\angle1$

Substitute $x = 37$ into the expression for $m\angle1$: $m\angle1=x + 32=37+32=69^{\circ}$.

Step6: Find the measure of $\angle2$

Substitute $x = 37$ into the expression for $m\angle2$: $m\angle2=3x=3\times37 = 111^{\circ}$.

Answer:

(a) Equation: $(x + 32)+3x=180$
(b) $m\angle1 = 69^{\circ}$
$m\angle2 = 111^{\circ}$