Question

∠1 and ∠2 are vertical angles. if m∠1=(5x−2)° and m∠2=(2x+10)°, then find the measure of ∠2.

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So, \(5x - 2=2x + 10\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(5x-2x - 2=2x-2x + 10\), which simplifies to \(3x-2 = 10\).
Add \(2\) to both sides: \(3x-2 + 2=10 + 2\), getting \(3x=12\).
Divide both sides by \(3\): \(x=\frac{12}{3}=4\).

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

Substitute \(x = 4\) into the expression for \(m\angle2\). \(m\angle2=(2x + 10)^{\circ}\), so \(m\angle2=(2\times4 + 10)^{\circ}=(8 + 10)^{\circ}=18^{\circ}\).

Answer:

\(18^{\circ}\)