Use the diagram to find the angle measures. Find m∠1, m∠3, and m∠4 if m∠2=117°.
Find the measures of all four angles if m∠2+m∠4=220°.

1.) m∠1 = 63 degree

m∠3 = 63 degree

m∠4 = 117 degree

m∠2 = 117 degree

2.) m∠1 = 70 degree

m∠3 = 70 degree

m∠4 = 110 degree

m∠2 = 110 degree

Step-by-step explanation:

Given that

1.) m∠2 = 117°.

In the figure, m∠1 is vertically opposite to m∠3, and m∠4 is vertically opposite to m∠2

Therefore, m∠2 = m∠4 = 117° ( because vertically opposite angle are equal)

Also, the sum of angles at a point is equal to 360 degrees

m∠2 + m∠4 = 234°

Take 234 away from 360. That is,

360 - 234 = 126

126/2 = 63 degrees.

Therefore, m∠1 = m∠3 = 63°

2.) If m∠2 + m∠4 = 220°

Subtract 220 from 360 since the sum of angles at a point is equal to 360 degrees

360 - 220 = 140

Divide 140 by 2 and also 220 by 2 to get

140/2 = 70 and 220/2 = 110

Therefore,

m∠1 = 70 degree

m∠3 = 70 degree

m∠4 = 110 degree

m∠2 = 110 degree

the answer will be the last one