Question

Diagonals of a quadrilateral $ABCD$ bisect each other. If $\angle A={45}^{\circ },$ then $\angle B$ equals

• A. ${45}^{\circ }$
• B. ${55}^{\circ }$
• C. ${135}^{\circ }$
• D. ${115}^{\circ }$

Answer 1

Answer: (C)

${135}^{\circ }$

The diagonal bisect each other. By parallelogram theorem, if the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Hence, ABCD is a parallelogram.
In a parallelogram, sum of adjacent angles is 180
$\angle A+\angle B=180$
$\angle B=180-45$
$\angle B={135}^{\circ }$