Question

In the given figure, BA || ED and BC || EF. Show that ∠ABC + ∠DEF = 180°.

Answer 1

Extend the line ED to meet the line BC at the point Z

We know that AB || EZ and BC is a transversal

From the figure we know that ∠ABZ and ∠EZB are interior angles

So we get

∠ABZ + ∠EZB = 180^o

∠ABZ can also be written as ∠ABC

∠ABC + ∠EZB = 180^o …… (1)

We know that EF || BC and EZ is a transversal

From the figure we know that ∠BZE and ∠ZEF are alternate angles

So we get

∠BZE = ∠ZEF

∠ZEF can also be written as ∠DEF

∠BZE = ∠DEF ….. (2)

By substituting equation (1) in (2) we get

∠ABC + ∠DEF = 180^o

Therefore, it is proved that ∠ABC + ∠DEF = 180^o