Question

HELP ME DO A STATEMENT REASON FOR THIS PLEASE

One of the same-side exterior angles formed by two lines and a transversal is equal to 1/6 of the right angle and is 11 times smaller than the other angle. Prove that the lines are parallel.

Answer 1

Lines are parallel if the sum of external angles of same side is 180°.

Explanation:

Let one of the external angle is α°.

and other external angle is β° which is equal to α°/11. (∵ Given on is 11 times smaller than the other.)

Also β° = 1/6 of the right angle = (1/6)×90° = 15°.

β° = α°/11 , ⇒ α° = 11×β° = 11×15° = 165°.

α°+β° = 165° + 15° = 180°.

Here, sum of the two external angles = 180° ⇔ the given lines are parallel.