Question

In the figure above A, B, C, D and E are concyclic points, O is the centre of the circle $\angle EAD={25}^{\circ }$ and $\angle CBD={20}^{\circ }$ Find $\angle EDC.$

• A. ${145}^{\circ }$
• B. ${180}^{\circ }$
• C. ${135}^{\circ }$
• D. ${85}^{\circ }$

Answer 1

The correct option is C ${135}^{\circ }$

$\angle OAB=\angle OBA$

As $O$ is the centre

$\angle BOA={90}^o$

$\therefore \angle ABD=\frac{\angle BDA}{2}$ (Angle substended by the chord is double)

$\Rightarrow \angle ABD={45}^o$

$\therefore \angle EDC={180}^o-{45}^o$

$\Rightarrow \angle EDC={135}^o$