Question

State true or false:

In the fig below. ABCD is a parallelogram. AF and CE are the bisectors of $\angle DAB$ and $\angle BCD$ respectively, then $\angle DCE=\frac{1}{2}\angle DCB$

• A. True
• B. False

Answer 1

The correct option is A True

$ABCD$ is a parallelogram and $CE$ is the bisector of $\angle BCD$
So, $\angle DCE=\angle BCE$
Now, $\angle BCD=\angle DCE+\angle BCE=\angle DCE+\angle DCE=2\angle DCE$
$\Rightarrow \angle DCE=\frac{1}{2}\angle BCD$