Question

Find x and fill in the angle values. Could you also explain how it works? Please and thank you.

Answer 1

Hello!

Angles 3 and 1 are vertical angles, and angles 2 and 4 are vertical angles. Vertical angles are congruent by definition, so angle 3 is congruent to angle 1, and angle 2 is congruent to angle 4.

The adjacent angles are supplementary (they add to equal 180 degrees) so you can set up an equation to solve for x.

180 = 2x + x
180 = 3x
60 = x

x = 60

To find the measure if each angle, plug in x as needed.

Angle 4 = x
Angle 4 = 60 degrees

Angle 2 = angle 4
Angle 2 = 60 degrees

Angle 3 = 2x
Angle 3 = 2(60)
Angle 3 = 120

Angle 1 = angle 3
Angle 1 = 120

I hope this helps you.