Question

The sum of adjacent angles of a parallelogram is

• A. ${180}^{\circ }$
• B. ${120}^{\circ }$
• C. ${360}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is A

${180}^{\circ }$

Explanation for the correct answer:

Property of parallelogram:
We will first consider a parallelogram $\mathrm{ABCD}$ and draw its figure to understand the question completely.

In the above figure quadrilateral $\mathrm{ABCD}$ is a parallelogram.

Then because the opposite sides of parallelogram are parallel therefore,

$\mathrm{AD}\parallel \mathrm{BC}$ and $\mathrm{AB}$ is transversal.

Now we know that Interior angles on the same side of the transversal are supplementary, that is they add to make ${180}^{\circ }$.
$\Rightarrow$ $\mathrm{A}+\mathrm{B}={180}^{\circ }$.
Similarly, applying the same concept we get,
$\Rightarrow$$\angle \mathrm{B}+\angle \mathrm{C}={180}^{\circ }$,

$\Rightarrow$$\angle \mathrm{C}+\angle \mathrm{D}={180}^{\circ }$ and

$\Rightarrow$$\angle \mathrm{D}+\angle \mathrm{A}={180}^{\circ }$

The sum of any two adjacent angles of a parallelogram is ${180}^{\circ }$.

Hence, option(A) is the correct answer.