### If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 4:5, then find the greater of the two angles.

**Answer:**

100°

**Step by Step Explanation:**

- Let x be the first interior angle on the same side of a transversal intersecting two parallel lines.
- We know that the sum of two interior angles on the same side of a transversal intersecting two parallel lines is 180°.

Thus, the second interior angle on the same side of a transversal intersecting two parallel lines = 180° - x

The ratio of the two interior angles on the same side of a transversal intersecting two parallel lines =x 180° - x - It is given that the ratio of the two interior angles on the same side of a transversal intersecting two parallel lines = 4:5

Therefore,

=x 180° - x 4 5

By cross multiplying, we get:

5x = 4(180° - x)

⇒ 5x = 4 × 180° - 4x

⇒ 5x + 4x = 720°

⇒ 9x = 720°

⇒ x =

°720 9

⇒ x = 80° - The first angle = 80°

The second angle = 180° - 80° = 100° - Hence, the greater of the two angles is
**100°**.