In each of the following figures, AB || CD and EF is a transversal. Find the value of x in each case.

(i)

(ii)

(iii)

(i)

From the figure,

The opposite angle of 5x° will be equal to 5x°. Because, they are vertically opposite angles.

Now, 5x° and 3x° are co-interior angles i.e., they lie inside the parallel lines on the same side of the transversal.

Co-interior angles are supplementary:

∴ 5x° + 3x° = 180°

⇒ 8x° = 180°

⇒ x° = $\dfrac{180^{\circ}}{8}$

x° = 22.5°

(ii)

From the figure,

The opposite angle of 5x° will be equal to 5x°. Because, they are vertically opposite angles.

5x° and 4x° are co-interior angles i.e., they lie inside the parallel lines on the same side of the transversal.

Co-interior angles are supplementary:

∴ 5x° + 4x° = 180°

⇒ 9x° = 180°

⇒ x° = $\dfrac{180^{\circ}}{9}$

x° = 20°

(iii)

From the figure,

140° and 4x° are corresponding angles i.e., they are in the same relative position at each intersection. Therefore, they are equal.

4x° = 140°

⇒ x° = $\dfrac{140^{\circ}}{4}$

x° = 35°