Question

in the figure, (mangle1=(x + 44)^{circ}) and (mangle2=(3x)^{circ}). (a) write an equation to find (x). make sure you use an \=\ sign in your answer. (b) find the degree measure of each angle.

Explanation:

Step1: Set up the equation

Angles ∠1 and ∠2 are supplementary (they form a straight - line), so their sum is 180°.
$(x + 44)+3x=180$

Step2: Combine like - terms

Combine the x terms on the left - hand side.
$x+3x + 44=180$
$4x+44 = 180$

Step3: Isolate the variable term

Subtract 44 from both sides of the equation.
$4x+44−44=180 - 44$
$4x=136$

Step4: Solve for x

Divide both sides by 4.
$\frac{4x}{4}=\frac{136}{4}$
$x = 34$

Step5: Find the measure of ∠1

Substitute x = 34 into the expression for m∠1.
$m\angle1=(x + 44)^{\circ}=(34 + 44)^{\circ}=78^{\circ}$

Step6: Find the measure of ∠2

Substitute x = 34 into the expression for m∠2.
$m\angle2=(3x)^{\circ}=(3\times34)^{\circ}=102^{\circ}$

Answer:

(a) Equation: $(x + 44)+3x=180$
(b) $m\angle1 = 78^{\circ}$
$m\angle2 = 102^{\circ}$