Question

in the figure, (mangle1=(3x)^{circ}) and (mangle2=(x + 36)^{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: Identify angle - relationship

Angles ∠1 and ∠2 are supplementary (linear - pair), so their sum is 180°.
$3x+(x + 36)=180$

Step2: Simplify the equation

Combine like - terms.
$3x+x+36 = 180$
$4x+36=180$

Step3: Solve for x

Subtract 36 from both sides.
$4x=180 - 36$
$4x=144$
Divide both sides by 4.
$x=\frac{144}{4}=36$

Step4: Find the measure of ∠1

Substitute x = 36 into the expression for ∠1.
$m\angle1=3x$
$m\angle1=3\times36 = 108^{\circ}$

Step5: Find the measure of ∠2

Substitute x = 36 into the expression for ∠2.
$m\angle2=x + 36$
$m\angle2=36+36=72^{\circ}$

Answer:

(a) Equation: $3x+(x + 36)=180$
(b) $m\angle1 = 108^{\circ}$
$m\angle2 = 72^{\circ}$