Question

The adjacent sides in the parallelogram are supplementary.
(A). True
(B). False

Answer 1

Hint: The given problem is related to the properties of a parallelogram. The opposite sides of the parallelogram are parallel and any of the remaining sides can act as a transversal. The adjacent angles will be co-interior angles, and the sum of co-interior angles is ${180}^o$ .

Complete step-by-step answer:

Let's consider the parallelogram ABCD.

Let’s consider the sides AD and BC. We know that the opposite sides of a parallelogram are parallel. So, AD ∥ BC . Now, as AD ∥ BC, we can consider the side AB as a transversal. We can see that the angles $\mathrm{\angle }A$ and $\mathrm{\angle }B$ lie between the parallel lines and on the same side of the transversal. So, $\mathrm{\angle }A$ and $\mathrm{\angle }B$ are co-interior angles. We know that the sum of the measure of the co-interior angles is equal to ${180}^o$ .
Therefore, $\mathrm{\angle }A+\mathrm{\angle }B={180}^o$. Now, we know that the angles whose sum is equal to ${180}^o$ are called supplementary angles. So, $\mathrm{\angle }A$ and $\mathrm{\angle }B$ are supplementary angles. But from the figure, we can see that $\mathrm{\angle }A$ and $\mathrm{\angle }B$ are adjacent angles of the parallelogram. So, we can say that the sum of any two adjacent angles of a parallelogram is ${180}^o$ . Hence, the given statement is true.

Note: Students generally get confused between complementary angles and supplementary angles. Because of this confusion, students can mark the answer as false, which is wrong. Complementary angles are the pair of angles, whose sum is ${90}^o$ , whereas supplementary angles are the pair of angles, whose sum is ${180}^o$ .