Question

∠1 and ∠2 are vertical angles. if m∠1=(4x + 13)° and m∠2=(3x + 30)°, then find themeasure of ∠2.

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So, \(m\angle1 = m\angle2\).
\(4x + 13=3x + 30\)

Step2: Solve for \(x\)

Subtract \(3x\) from both sides:
\(4x-3x + 13=3x-3x + 30\)
\(x+13 = 30\)
Subtract 13 from both sides:
\(x+13-13=30 - 13\)
\(x = 17\)

Step3: Find \(m\angle2\)

Substitute \(x = 17\) into \(m\angle2=(3x + 30)^{\circ}\)
\(m\angle2=(3\times17+30)^{\circ}\)
\(m\angle2=(51 + 30)^{\circ}\)
\(m\angle2 = 81^{\circ}\)

Answer:

\(81^{\circ}\)