given: m||n ; j||k prove: m∠1+m∠4=180

Question

STATEMENTS

m || n ; j || k

∠1 ≅ ∠2

∠3 ≅ ∠4

m∠1 =  m∠2 ; m∠3 =  m∠4

m∠2 +  m∠3 = 180

m∠1 +  m∠4 = 180

Answer 1

The reasons are:

∠1 ≅ ∠2 Corresponding angles are congruent

∠3 ≅ ∠4 Vertical angles are congruent

m∠1 =  m∠2 ; m∠3 =  m∠4 Definition of Congruent Angles

m∠2 +  m∠3 = 180 Consecutive interior angles are supplementary

m∠1 +  m∠4 = 180 Substitution (substituted angle 1 for 2, and 4 for 3)

Answer 2

Since both pairs are parallel; opposite and corresponding angles are =.

So <4=the corresponding angle on "m"; making a straight line which=180°.