Question

Prove that adjacent angles of parallelogram are supplimentry.

Answer 1

Let ABCD be a parallelogram.

Then AD$||$BC & AB is transversal.

Therefore, $A+B={180}^o$[since, sum of the interior angles on the same since of the transversal is ${180}^o$]

Similarly, $\angle B+\angle C={180}^o$, $\angle C+\angle D={180}^o$ & $\angle D+\angle A={180}^o$

Thus, the sum of any $2$ adjacent angles of a parallelogram is ${180}^o$. Hence any $2$ adjacent angles of a parallelogram are supplementary.