Question

∠1 and ∠2 are supplementary angles. if (mangle1=(2x + 27)^{circ}) and (mangle2=(2x - 3)^{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, $(2x + 27)+(2x - 3)=180$.

Step2: Simplify the left - hand side

Combine like terms: $2x+2x + 27-3=180$, which gives $4x+24 = 180$.

Step3: Solve for $x$

Subtract 24 from both sides: $4x=180 - 24=156$. Then divide both sides by 4: $x=\frac{156}{4}=39$.

Step4: Find the measure of $\angle2$

Substitute $x = 39$ into the expression for $m\angle2$. $m\angle2=(2x - 3)^{\circ}=(2\times39-3)^{\circ}=(78 - 3)^{\circ}=75^{\circ}$.

Answer:

$75^{\circ}$