Question

∠1 and ∠2 are vertical angles. if (mangle1=(4x - 10)^{circ}) and (mangle2=(2x + 2)^{circ}), then find the measure of ∠2.

Explanation:

Step1: Set up the equation

Since vertical - angles are equal, we set \(m\angle1 = m\angle2\). So, \(4x−10 = 2x + 2\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(4x-2x−10=2x - 2x+2\), which simplifies to \(2x−10 = 2\). Then add 10 to both sides: \(2x-10 + 10=2 + 10\), getting \(2x=12\). Divide both sides by 2: \(x=\frac{12}{2}=6\).

Step3: Find the measure of \(\angle2\)

Substitute \(x = 6\) into the expression for \(m\angle2\). \(m\angle2=(2x + 2)^{\circ}=(2\times6 + 2)^{\circ}=(12 + 2)^{\circ}=14^{\circ}\).

Answer:

\(14^{\circ}\)