Question

find the measure of angle 2.

Explanation:

Step1: Identify angle - pair relationship

Angles \(4x + 84\) and \(6x+62\) are vertical angles, and vertical angles are equal. So we set up the equation \(4x + 84=6x + 62\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(84 = 2x+62\). Then subtract 62 from both sides: \(2x=84 - 62=22\). Divide both sides by 2: \(x = 11\).

Step3: Find the measure of angle 2

Angle 2 is equal to \(4x + 84\) (or \(6x + 62\) since they are vertical - angles). Substitute \(x = 11\) into \(4x + 84\). We get \(4\times11+84=44 + 84=128\).

Answer:

128