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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
Options
54°
120°
108°
136°
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°
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