Question

In the given figure, arms BA and BC of ∠ABC are respectively parallel to arms ED and EF of ∠DEF. Prove that ∠ABC + ∠DEF = 180°

Answer 1

The figure is given as follows:

It is given that, arms BA and BC of are respectively parallel to arms ED and EF of .

We need to show that

Let us extend BC to meet ED at point P.

We haveand. So, and are corresponding angles, these two should be equal.

Therefore,

Also, we have. So, and are consecutive interior angles, these two must be supplementary.

Therefore,

Hence proved.