MCQ

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

#### Options

54°

120°

108°

136°

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#### Solution

Let us draw the following figure:

Here AB || CD with *t* as a transversal.

Also, ∠1and ∠2are the two angles on the same side of the transversal.

It is given that

∠1:∠2 = 2:3

Therefore, let

∠1 = 2x

and ∠2 = 3x

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

Therefore,

∠1 + ∠2 = 180°

On substituting ∠1 =2x and ∠2 = 3x in equation above, we get:

2x +3x = 180°

5x = 180°

`x = (180°) /5`

x = 36°

Clearly, 3x >2x

Therefore,

∠2 > ∠1

Also,

∠2 = 3x

∠2 = 3(36°)

∠2 = 108°

Concept: Parallel Lines and a Transversal

Is there an error in this question or solution?

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