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
a) 54°
b) 108°
c) 120°
d) 136°

Solution:

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

We have to find the greater of the two angles.

Let one angle be 2x

Let the other angle be 3x

We know that the sum of interior angles on the same side of a transversal intersecting two parallel lines is 180°

So, 2x + 3x = 180°

5x = 180°

x = 180°/5

x = 36°

Now, measure of one angle = 2(36°) = 72°

Measure of other angle = 3(36°) = 108°

Therefore, the greater of the two angle is 108°

✦ Try This: Can two right angles form a linear pair?

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6

NCERT Exemplar Class 9 Maths Exercise 6.1 Sample Problem 1

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 a) 54°, b) 108°, c) 120°, d) 136°

Summary:

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 108°

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