Question

In the given figure, ABCD is a cyclic Quadrilateral. O is the centre of the circle and $\angle BOD={160}^{\circ }$, find the measure of $\angle BPD.$

• A. ${50}^{\circ }$
• B. ${20}^{\circ }$
• C. ${100}^{\circ }$
• D. ${70}^{\circ }$

Answer 1

The correct option is C ${100}^{\circ }$

Consider the arc BCD of the circle. This arc makes angle $\angle BOD={160}^{\circ }$ at the centre of the circle and $\angle BAD$ at a point A on the circumference.



$\therefore \angle BAD=\frac{1}{2}\angle BOD={80}^{\circ }$
Now, ABPD is a cyclic quadrilateral.
$\Rightarrow \angle BAD+\angle BPD={180}^{\circ }\Rightarrow {80}^{\circ }+\angle BPD={180}^{\circ }\Rightarrow \angle BPD={100}^{\circ }$