Question

In the given figure, AB || CD || EF and GH || KL. The measure of ∠HKL is

(a) 85°

(b) 135°

(c) 145°

(d) 215°

Answer 1

The given figure is as follows:

Let us extend GH to meet AB at Y.

We have the following:

and are the supplementary angles. Therefore,

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

Therefore,

Since, . Thus, and are the corresponding angles.

Therefore,

From (1), we get:

……(3)

Since . Thus are corresponding angles,

Therefore,

Thus, the required angle x can be calculated as:

From (3) and (4) we get:

Hence, the correct choice is (c).