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

Step-by-step 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.

∠∠∠∠∠

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.