Question

∠1 and ∠2 are vertical angles. if ( mangle1=(4x + 3)^{circ} ) and ( mangle2=(2x + 15)^{circ} ), then find the measure of ∠1.

Explanation:

Step1: Set up the equation

Since vertical angles are equal, \(4x + 3=2x + 15\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(4x-2x + 3=2x-2x + 15\), which simplifies to \(2x+3 = 15\).
Subtract \(3\) from both sides: \(2x+3 - 3=15 - 3\), so \(2x=12\).
Divide both sides by \(2\): \(x=\frac{12}{2}=6\).

Step3: Find the measure of \(\angle1\)

Substitute \(x = 6\) into \(m\angle1=(4x + 3)^{\circ}\).
\(m\angle1=(4\times6+3)^{\circ}=(24 + 3)^{\circ}=27^{\circ}\).

Answer:

\(27^{\circ}\)