In figure 5.30 lines AB, CD and EF are parallel.

Find ∠x, ∠y, ∠z and ∠p

Given:

AB, CD, EF are parallel lines

Theory.

Straight line possesses 180° angle

If 2 lines are parallel then corresponding angles are equal.

As CD || EF

And DF is the transverse

By corresponding angles

⇒ ∠ z = 58°

As DF is a straight line

∠ z + ∠ p = 180°

⇒ ∠ p = 180° - 58° = 122°

As AB || CD

By corresponding angles

⇒ ∠ y = ∠ p = 122°

As AB is straight line

∠ x + ∠ y = 180°

⇒ ∠ x = 180° - 122° = 58°