Question

∠1 and ∠2 are vertical angles. if ( m∠1=(2x + 20)^{circ} ) and ( m∠2=(7x - 5)^{circ} ), then find the measure of ∠2.

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So, \(m\angle1 = m\angle2\).
\(2x + 20=7x - 5\)

Step2: Solve for \(x\)

Subtract \(2x\) from both sides:
\(20 = 5x-5\)
Add \(5\) to both sides:
\(25 = 5x\)
Divide both sides by \(5\):
\(x = 5\)

Step3: Find \(m\angle2\)

Substitute \(x = 5\) into \(m\angle2=(7x - 5)^{\circ}\)
\(m\angle2=(7\times5 - 5)^{\circ}=(35 - 5)^{\circ}=30^{\circ}\)

Answer:

\(30^{\circ}\)