Question

In the given figure, if l₁ || l₂, what is x + y in terms of w and z?

Options

• 180° − w + z

•  180° + w − z

•  180° - w − z

•  180° + w + z

Answer 1

The figure is given below:

Since, y and z are alternate interior opposite angles. Therefore, these must be equal.

 y = z (i)

Also x and w are consecutive interior angles.

Theorem states: If a transversal intersects two parallel lines, then each pair of consecutive interior angles are supplementary.

Therefore,

 x +w = 180° (ii)

On adding equation (i) and (iii) , we get :

x + y + w = 180°

x + y = 180° + z - w