Question

In the given figure, show that AB || EF.

Answer 1

The figure is given as follows:

We need to prove that.

It is given that and

$$\begin{gathered} \angle ACD=\angle ACE+\angle ECD \\ \angle ACD=22°+35° \\ \angle ACD=57° \end{gathered}$$

Thus,

But these are the pair of alternate interior opposite angles.

Theorem states: If a transversal intersects two lines in such a way that a pair of alternate interior angles is equal, then the two lines are parallel.

Therefore,

(i)

It is given that and

Thus,

But these are the pair of consecutive interior opposite angles.

Theorem states: If a transversal intersects two lines in such a way that a pair of consecutive interior angles is supplementary, then the two lines are parallel.

Therefore,

(ii)

From (i) and (ii), we get:

Hence proved.