Question

Consider the cyclic quadrilateral ABCD. If O is the centre of the circle and $\angle$BOD = ${160}^{\circ }$, then find the measure of $\angle$BPD.

• A. ${100}^{\circ }$
• B. ${80}^{\circ }$
• C. ${90}^{\circ }$
• D. ${70}^{\circ }$

Answer 1

The correct option is A

${100}^{\circ }$

We know that the angle subtended by an arc at the centre of a circle is double the angle subtended by it on any remaining part of the circle.

$⟹\angle BAD=\frac{\angle BOD}{2}={80}^{\circ }$

Consider the cyclic quadrilateral ABPD. Since the opposite angles are supplementary,

$\angle BAD+\angle BPD={180}^{\circ }$

i.e., ${80}^{\circ }+\angle BPD={180}^{\circ }$

$⟹\angle BPD={100}^{\circ }$