Question

∠1 and ∠2 are vertical angles. if m∠1=(4x + 22)° and m∠2=(6x + 10)°, then find the measure of ∠2.

Explanation:

Step1: Set the two angle - measures equal

Since vertical angles are congruent, we set \(m\angle1=m\angle2\). So, \(4x + 22=6x+10\).

Step2: Solve for \(x\)

Subtract \(4x\) from both sides: \(22 = 2x+10\). Then subtract 10 from both sides: \(22 - 10=2x\), which gives \(12 = 2x\). Divide both sides by 2: \(x = 6\).

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

Substitute \(x = 6\) into the expression for \(m\angle2\). \(m\angle2=(6x + 10)^{\circ}=(6\times6 + 10)^{\circ}=(36+10)^{\circ}=46^{\circ}\).

Answer:

\(46^{\circ}\)