Question

1. given: < 1 = 3x + 13 < 2 = 4x + 2 < 1 and < 2 are vertical angles find: the measure of each angle.

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So, \(3x + 13=4x + 2\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(13=x + 2\).
Then subtract \(2\) from both sides: \(x=13 - 2=11\).

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

Substitute \(x = 11\) into \(3x+13\): \(3\times11 + 13=33+13 = 46\).

Step4: Find the measure of \(\angle2\)

Substitute \(x = 11\) into \(4x + 2\): \(4\times11+2=44 + 2=46\).

Answer:

The measure of \(\angle1\) is \(46^{\circ}\) and the measure of \(\angle2\) is \(46^{\circ}\).