Question

Calculate the measure of $\angle AOC.$

Answer 1

Join AC.
In $\Delta AOB,$

OA = OB (radii of same circle)

$\angle OAB=\angle OBA={40}^{\circ }$

In $\Delta OBC$,

OC = OB (radii of same circle)

$\angle OCB=\angle OBC={30}^{\circ }$

Now,

$\angle ABC=\angle ABD+\angle OBC$

$=40+30={70}^{\circ }$

$\angle AOC=2\angle ABC=2\times 70={140}^{\circ }$