Question

In the given figure, AB || CD || EF and GH || KL. Find the ∠HKL.

Answer 1

The given figure is as follows:

Let us extend GH to meet AB at Y.

Similarly, extend LK to meet CD at Z.

We have the following:

and are the vertically opposite angles. Therefore,

Since, . Thus,and are the consecutive interior angles.

Therefore,

From (i), we get:

Since,. Thus,and are the corresponding angles.

Therefore,

From (ii), we get:

(iii)

Also,and are the alternate interior opposite angles.

Therefore,

(iv)

Thus, the required angle can be calculated as:

From (iii) and (iv) we get:

Hence, the required value for is.