Question

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2:3, then the measure of the larger angle is

(a) 54°

(b) 120°

(c) 108°

(d) 136°

Answer 1

Let us draw the following figure:

Here with t as a transversal.

Also, and are the two angles on the same side of the transversal.

It is given that

Therefore, let

and

We also, know that, if a transversal intersects two parallel lines, then each pair of consecutive interior angles are supplementary.

Therefore,

On substituting andin equation above, we get:

Clearly,

Therefore,

Also,

Hence, the correct choice is (c).