Question

find the measure of angle 3.

Explanation:

Step1: Identify angle - pair relationship

The angle of 116° and the angle labeled \(6x + 2\) are vertical angles. Vertical angles are equal. So, \(6x+2=116\).

Step2: Solve for \(x\)

Subtract 2 from both sides of the equation: \(6x=116 - 2\), so \(6x=114\). Then divide both sides by 6: \(x=\frac{114}{6}=19\).

Step3: Find angle 3

Angle 3 and the angle \(6x + 2\) are corresponding angles. Corresponding angles are equal when two lines are parallel. Since \(6x+2 = 116^{\circ}\), angle 3 is also \(116^{\circ}\).

Answer:

\(116^{\circ}\)