### 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.

100°

Step by Step Explanation:
1. Let x be the first interior angle on the same side of a transversal intersecting two parallel lines.
2. 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

3. 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°
4. The first angle = 80°
The second angle = 180° - 80° = 100°
5. Hence, the greater of the two angles is 100°.