Question

∠1 and ∠2 are vertical angles. if ( m∠1=(4x + 2)^circ ) and ( m∠2=(x + 17)^circ ), then find the measure of ∠2.

Explanation:

Step1: Set up the equation

Since vertical angles are equal, \(4x + 2=x + 17\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(4x - x+ 2=x - x+ 17\), so \(3x + 2 = 17\).
Subtract \(2\) from both sides: \(3x+2 - 2=17 - 2\), so \(3x=15\).
Divide both sides by \(3\): \(x=\frac{15}{3}=5\).

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

Substitute \(x = 5\) into \(m\angle2=(x + 17)^{\circ}\). Then \(m\angle2=(5 + 17)^{\circ}=22^{\circ}\).

Answer:

\(22\)