Question

∠1 and ∠2 are supplementary angles. if (mangle1=(x - 29)^{circ}) and (mangle2=(2x - 13)^{circ}), then find the measure of ∠1.

Explanation:

Step1: Use supplementary - angle property

Supplementary angles add up to 180°. So, $m\angle1 + m\angle2=180^{\circ}$.
Substitute the given expressions: $(x - 29)+(2x - 13)=180$.

Step2: Simplify the left - hand side

Combine like terms: $x+2x-29 - 13 = 180$, which gives $3x-42 = 180$.

Step3: Solve for x

Add 42 to both sides: $3x=180 + 42$, so $3x=222$.
Divide both sides by 3: $x=\frac{222}{3}=74$.

Step4: Find the measure of $\angle1$

Substitute $x = 74$ into the expression for $m\angle1$: $m\angle1=(x - 29)^{\circ}=(74 - 29)^{\circ}=45^{\circ}$.

Answer:

$45^{\circ}$