Find the value of x for which l is parallel to m. The diagram is not to scale.

Solution:

From the figure given, line ‘l’ is parallel to ‘m’.

∠ABC and ∠BAD are called alternate angles formed by transversal AB.

The alternate angles are formed between the parallel lines after they are cut by a transversal.

When two straight lines are cut by a transversal, then the angles formed on the opposite side of the transversal with respect to both the lines are called alternate angles.

So, alternate angles are those angles that have different vertices and lie on the alternate sides of the transversal.

Hence, ∠ABC = ∠BAD

⇒ 3x - 43° = 80°

⇒ 3x = 123°

⇒ x = 41°

Find the value of x for which l is parallel to m. The diagram is not to scale.

Summary:

From the given figure where l and m are parallel, the value of x is 41°.