Question

In the given figure, $O$ is the centre, the cirlcle. The angle subended by the are $BCD$ at the centre is ${144}^o$, $BC$ is produced to $P$. Determine $\angle BAD$ and $\angle DCP$

Answer 1

REF.image

Sine, $\angle BAD$= Half of $\angle BOD$.

[Angle suspended by an arc on center is double that of the circumference]

So.$\angle BAD=144/2={72}^{\circ }$

$\therefore \angle BCD=180-{72}^{\circ }$

[Sum of the opposite angle of a cyclic quadrilateral is ${180}^{\circ }]$

so $\angle BCD={108}^{\circ }$

so,$\angle DCP={180}^{\circ }-{108}^{\circ }={72}^{\circ }$

[Linear pair].