Question

Diagonals of quadrilateral ABCD bisect each other and $\angle B={75}^{\circ }$ ,then the value of $\angle A$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Diagonals of quadrilateral ABCD bisect each other, then it is a parallelogram

Sum of two adjacent angles of parallelogram is ${180}^{\circ }$
$\angle A+\angle B={180}^{\circ }$
$\angle A={180}^{\circ }-{75}^{\circ }$
$\angle A={105}^{\circ }$
Hence, the value of $\angle A$ is ${105}^{\circ }$