Question

In the given figure, ABCD and ABPD are two cyclic quadrilaterals.

If $\angle BOD={160}^{\circ }$, find the difference of $\angle BPDand\angle BCD.$

• A.
• B.
• C.
• D.

Answer 1

The correct option is C


Here, concept used: opposite angles of a cyclic quadrilateral are supplementary.
$So,\angle BPD+\angle BAD={180}^{\circ }\to \left(1\right)\to \angle BCD+\angle BAD={180}^{\circ }\to \left(2\right)$
From (1) and (2), we get:
$\angle BPD+\angle BAD=\angle BCD+\angle BAD={180}^{\circ }\to \angle BPD=\angle BCD$ (subtracting $\angle BAD$ from both sides)
So, difference between $\angle BPDand\angle BCD=0^{\circ }$