Question

If PQRS is a parallelogram, then $\angle Q - \angle S$ is equal to:
A) ${90^0}$
B) ${120^0}$
C) ${180^0}$
D) ${0^0}$

Answer 1

Hint: According to the question given in the question we have to determine the difference between the angles $\angle Q - \angle S$ for a parallelogram PQRS. So, first of all we have to draw the diagram of a parallelogram PQRS which is as below:

Now, we have to understand about the parallelogram which is explained as below:
A parallelogram is a type of quadrilateral that has equal and parallel opposite sides and for the given parallelogram PQRS as above, where, PQ is equal to RS and PR is equal to QS
In the parallelogram PQRS line PQ is parallel to the line to RS and line PR is parallel to the line QS.

Complete step-by-step solution:
Step 1: First of all we have to draw the diagram for the given parallelogram PQRS as mentioned in the solution hint. Hence,

Step 2: In the parallelogram PQRS as we all know that PQ is equal to RS and PR is equal to QS and line PQ is parallel to the line to RS and line PR is parallel to the line QS and opposite angles in the parallelogram PQRS are equal. Hence,
$
   \Rightarrow \angle P = \angle R, \\
   \Rightarrow \angle Q = \angle S
 $
Step 3: Now, we can obtain the difference of the angles $\angle Q - \angle S$ for the given parallelogram PQRS.
$
   \Rightarrow \angle Q - \angle S = \angle Q - \angle Q \\
   = 0
 $
Hence, we have obtained the difference between the angles $\angle Q - \angle S$ for the given parallelogram PQRS which is 0.

Therefore option (D) is correct.

Note: The opposite sides of the parallelogram are parallel to each other.
The opposite sides of the parallelogram are equal in length and the opposite angles of parallelogram are equal in measure.