Question

In a parallelogram, the sum of adjacent angles is:

• A. ${90}^{\circ }$
• B. ${180}^{\circ }$
• C. ${270}^{\circ }$
• D. ${360}^{\circ }$

Answer 1

The correct option is B ${180}^{\circ }$

$ABCD$ is a parallelogram.

$\therefore$ $AB$ $\parallel$ $DC$ and $AD$ $\parallel BC$

$\therefore$ $\angle$$d$ $+$ $\angle$ $e$ (corresponding angle)

$\angle$$a$ $+$ $\angle e$ = $180$${}^{\circ }$ (supplementary angle or linear pair)

$\angle$$a$ $+$ $\angle$$d$ = 180${}^{\circ }$ ($\because$ $\angle$$d$ = $\angle$$e$)

$\therefore$ sum of adjacent angle are $180$${}^{\circ }$

Ans : B)$180$${}^{\circ }$