Question

∠1 and ∠2 are vertical angles. if ( mangle1=(4x - 9)^{circ} ) and ( mangle2=(3x + 27)^{circ} ), then find the measure of ∠1.

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(4x - 9=3x + 27\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(4x-3x - 9=3x-3x + 27\), which gives \(x-9 = 27\).
Add \(9\) to both sides: \(x-9 + 9=27+9\), so \(x = 36\).

Step3: Find \(m\angle1\)

Substitute \(x = 36\) into \(m\angle1=(4x - 9)^{\circ}\).
\(m\angle1=(4\times36-9)^{\circ}=(144 - 9)^{\circ}=135^{\circ}\).

Answer:

\(135^{\circ}\)