Question

State true or false:

In the following figure, $ABCD$ is a parallelogram, then

$\angle DAP+\angle CBP=\angle APB$

• A. True
• B. False

Answer 1

The correct option is A True

ABCD is a parallelogram.
Draw a line PQ which is parallel to AD as well as BC.
$\angle DAP=\angle APQ$ (Alternate interior angles are equal)......(1)
Similarly,
$\angle CBP=\angle BPQ$ (Alternate interior angles are equal)......(2)
Add equation (1) and (2)
$\angle DAP+\angle CBP=\angle APQ+\angle BPQ$
$=>\angle DAP+\angle CBP=\angle APB$