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

Correct option is A

Given:
If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2 : 3
Concept Used:
We also, know that, if a transversal intersects two parallel lines, then each pair of consecutive interior angles are supplementary.
Therefore,

​$$\angle 1 + \angle 2 = 180 \degree$$ 

Solution:

According to given condition.

​$${\angle} 1 = 2x \,\text{and}\, \angle 2 = 3x$$

We know

​$$\angle 1 + \angle 2 = 180 \degree\\2x+3x = 180 \degree\\5x= 180 \degree\\x = 36 \degree\\$$

$$\angle 1 = 2x = 2 \times 36 = 72\degree\\\angle 2 = 3x = 2 \times 36 = 108\degree\\$$​​

SO, the greater angle is 108$$\degree$$​​