Question

Help please. (Given: y ∥ x Prove: m∠5 + m∠2 + m∠6 = 180)

Answer 1

The answers are below. Hope this helped. I sacrificed my answers ˙-˙ :)

Explanation:

<1 congruent to <5 Given

<3 congruent to <6 Alternate Interior Angles theorem

m<1 = m<5 Alternate Interior Angles theorem

m<3 = m<6 Definition of congruent angles

m<1+m<2+m<3=m< LAM Definition of congruent angles

m<1+m<2+m<3=180 Angle additon postulate

m<5+m<2+m<6=180 Definition of straight angle

Answer 2

Explanation:

Concepts used :

sum of angles at a point on straight line is 180

if a transversal intersects two parallel lines then alternate angles are equal.

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∠∠∠∠∠

m∠1 + m∠2 + m∠3 = 180 ____________(A)

reason :sum of angles at a point on straight line is 180

these angles lie on LAM at point A

m∠1 = m∠5

Reason: alternate angles y ∥ x and AC is transversal

m∠3 = m∠6

Reason: alternate angles y ∥ x and AB is transversal

Substituting m∠1 with m∠5 and m∠3 with m∠6

in equation A---m∠1 + m∠2 + m∠3 = 180

m∠5 + m∠2 + m∠6 = 180

Hence proved.