Question

This is geometrey and this < is the angle symbol. Please help!

Complete the reasons for proof.

Given
M<3=M<4

To prove
<1,<2 are supplementary

I have a fill in the blank section that I can type if need be! Please help me.

Answer 1

Given: ∠3 = ∠4

1) ∠1 = ∠4 because of vertical angles

2) ∠4 = ∠3, given

3) So ∠1 = ∠4 = ∠3, so ∠1 = ∠3, because of transitive property

2) ∠3 + ∠2 = 180 degrees because definition of a straight line

3) ∠1 + ∠2 = 180 degrees, using substitution

4) Since ∠1 + ∠2 adds up to 180 degrees, that makes them supplementary angles.