In quadrilateral PQRS below, sides PS and QR are parallel for what value of x?

Solution:

Consecutive interior angles are defined as the pair of non adjacent interior angles that lie on the same side of the transversal. 

The word 'consecutive' refers to things that appear next to each other.

Given, PQRS is a quadrilateral with sides PS and QR parallel.

In any quadrilateral the sum of interior angles should sum up to 360°

From the figure, ∠P = 70° and ∠S = 112°

We have to find the value of x.

From the figure, x = ∠Q

∠P + ∠Q = 180°

70° + ∠Q = 180°

∠Q = 180° - 70°

∠Q = 110°

Similarly, ∠R + ∠S = 180°

∠R + 112° = 180°

∠R = 180° - 112°

∠R = 68°

Verification:

Sum of interior angles should be equal to 360°.

∠P + ∠Q + ∠R + ∠S = 70° + 110° + 68° + 112°

= 180° + 180°

= 360°

Therefore, the value of x is 110°.

In quadrilateral PQRS below, sides PS and QR are parallel for what value of x?

Summary:

In quadrilateral PQRS below, sides PS and QR are parallel for the value of x = 110°.