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: Recall supplementary - angle property

Supplementary angles add up to 180°. So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(2x + 27)^{\circ}\) and \(m\angle2=(2x - 3)^{\circ}\) into the equation: \((2x + 27)+(2x - 3)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+2x+27 - 3=180\), which simplifies to \(4x + 24=180\).

Step3: Solve for \(x\)

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

Step4: Find the measure of \(\angle2\)

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

Answer:

\(75^{\circ}\)