Question

Two parallel lines are cut by a transversal. For each pair of interior angles on the same side of the transversal, if one angle exceeds the twice of the other angle by 48°. Find the angles

Answer 1

Let the two parallel lines be m and n and l be the transversal

Let one of the interior angles on the same side of the transversal be x

Then the other will be 2x + 48°

We know that they are supplementary.

∴ x + (2x + 48°) = 180°

x + 2x + 48° = 180°

3x + 48° = 180°

3x + 48° − 48° = 180° − 48°

3x = 132°

x = `(132^circ)/3`

x = 44°

∴ One angle is x = 44°

Other angel is 2x + 48° = 2(44) + 48°

= 88 + 48°

= 136°

∴ The angles are 44° and 136°