Question

If a transversal intersects two parallel lines, and the difference of two interior angles on the same side of a transversal is 20°, find the angles.

Answer 1

Let the two interior angles on the same side of the transversal be x and y.

Given, their difference is 20°.

∴ x – y = 20°

⇒ y = x – 20°  ......(i)

Since, l and m are parallel and P is transversal

Then, x + y = 180°  ......[∵ Sum of an interior angles is 180°]

∴ x + x – 20° = 180°  ......[From equation (i)]

⇒ 2x = 180° + 20°

⇒ 2x = 200°

⇒ x = `200^circ/2` = 100°

Now, y = x – 20°

∴ y = 100° – 20° = 80°

Therefore, the angles are 100° and 80°, respectively.