Question

The diagonals AC and BD of a parallelogram ABCD interest each other at the point O. If $\angle DAC={30}^0$ and $\angle AOB={72}^0$, then find $\angle DBC$.

Answer 1

$ABCD$ is a parallelogram.

Therefore,

$AD\parallel BC$

$\Rightarrow \angle ACB=\angle DAC=30°$

Now, $\angle AOB$ is an exterior angle of $△BOC$.

As we know that exterior angle is equal to the sum of two interior opposite interior angles.

Therefore,

$\angle OBC+\angle OCB=\angle AOB$

$\Rightarrow \angle OBC+30°=72°$

$\Rightarrow \angle OBC=72°-30°=42°$

$\therefore \angle DBC=\angle OBC=42°$

Hence $\angle DBC$ is $42°$.