Question

If the bisectors of two adjacent angles A and B of a quadrilateral ABCD intersect at a point O such that $\angle C+\angle D=k\angle AOB$, then the value of $k$ is $2.$

• A. True
• B. False

Answer 1

The correct option is A True

$\angle A+\angle B+\angle C+\angle D={360}^o$ .....(1)

In $△AOB$,

$\angle AOB+\frac{\angle A}{2}+\frac{\angle B}{2}={180}^o$

$2\angle AOB+\angle A+\angle B={360}^o$

$\angle A+\angle B={360}^o-2\angle AOB$ .......(2)

Substituting (2) in (1),

${360}^o-2\angle AOB+\angle C+\angle D={360}^o$

$2\angle AOB=\angle C+\angle D$

Comparing with $\angle C+\angle D=k\angle AOB$,

we get, $k=2$