Given: When two lines are crossed by the transversal, a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal are called alternate interior angles. We know that, each pair of alternate interior angles are equal. Here, X and Y are alternate angle and they are equal. That is, X = Y = 50 ° Yes l ∥ m Since, X and Y angles are equal and they are alternate interior angles l ∥ m .

Given: When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other. Here, y and z are vertically opposite angles Therefore, y = z ⇒ y = 130 ° Now, if two parallel lines are cut by a transversal, then each pair of interior angles on the same side of the transversal are supplementary. x and y are a pair of interior angles on the same side of the transversal. Then, x + y = 180 ° Yes l ∥ m , because x + y = 180 ° .