Question

∠1 and ∠2 are supplementary angles. if (mangle1=(4x - 4)^{circ}) and (mangle2=(3x + 30)^{circ}), then find the measure of ∠2.

Explanation:

Step1: Use supplementary - angle property

Since $\angle1$ and $\angle2$ are supplementary, $m\angle1 + m\angle2=180^{\circ}$. So, $(4x - 4)+(3x + 30)=180$.

Step2: Simplify the left - hand side

Combine like terms: $4x+3x-4 + 30=180$, which gives $7x+26 = 180$.

Step3: Solve for $x$

Subtract 26 from both sides: $7x=180 - 26=154$. Then divide both sides by 7: $x=\frac{154}{7}=22$.

Step4: Find the measure of $\angle2$

Substitute $x = 22$ into the expression for $m\angle2$: $m\angle2=(3x + 30)^{\circ}=(3\times22+30)^{\circ}=(66 + 30)^{\circ}=96^{\circ}$.

Answer:

$96^{\circ}$