Question

$\angle 1$ and $\angle 2$ are vertical angles. if $m\angle 1 = (5x + 24)^\circ$ and $m\angle 2 = (7x + 8)^\circ$, then find the measure of $\angle 2$.

Explanation:

Step1: Set up equation

Since vertical angles are equal, \(5x + 24=7x + 8\).

Step2: Solve for \(x\)

Subtract \(5x\) from both sides: \(24 = 2x+8\).
Subtract \(8\) from both sides: \(16 = 2x\).
Divide both sides by \(2\): \(x = 8\).

Step3: Find \(m\angle2\)

Substitute \(x = 8\) into \(m\angle2=(7x + 8)^{\circ}\).
\(m\angle2=(7\times8 + 8)^{\circ}=(56 + 8)^{\circ}=64^{\circ}\).

Answer:

\(64^{\circ}\)