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) `54^0` (b)`120^0` (c) `108^0` (d) `136^0`

Explanation

Solution
Two interior angles on the same side of a transversal intersecting two parallellines are in the ratio `2 : 3` (Given)
Let one angle = `2x`Other angle = `3x`
As sum of interior angles on same side of transversal intersecting two parallel line is `180^0`
`2x = 3x = 180^0`
⇒ `5x = 180^0`
`:.x =180^0/5 =36^0`
Hence, two angles are `2x = 2 × 36 = 72`
`3x = 3 × 36 = 108^0`
Hence, greater angle is `108°`.