Given: m<1 + m<2 + m<3 = 180; m<3+m<4=180

Question

prove:m<1+m<2=m<4

Answer 1

m∠1 = Angle 1

m∠2 = Angle 2

m∠3 = Angle 3

m∠4 = Angle 4

m∠3 + m∠4 = 180°

Subtract m∠4 to both sides

m∠3 = 180° - m∠4

Put this value in equation:

m∠1 + m∠2 + m∠3 = 180°

m∠1 + m∠2 + 180° - m∠4 = 180°

Subtract 180° to both sides

m∠1 + m∠2 - m∠4 = 0

Add m∠4 to both sides

m∠1 + m∠2 = m∠4