Question

In the adjacent figure, O is the centre of the circle. Find the value of x.

Answer 1

$\angle OCD={90}^{\circ }-{70}^{\circ }={20}^{\circ }$
$\angle ODC={20}^{\circ }(\because \Delta ODC$ is isosceles tringle)
$\Rightarrow \angle DOC={180}^{\circ }-20\times 20-={140}^{\circ }$
$\therefore \angle DOA={70}^{\circ }$
$\Rightarrow \angle DOB={180}^{\circ }-{70}^{\circ }={110}^{\circ }$
$\Rightarrow \angle DAB=x=\frac{{110}^{\circ }}{2}={55}^{\circ }$ (angle is segment $=\frac{1}{2}$ angle at center)
${55}^{\circ }$