What is the value of $\angle AOC$ if $ABCD$ is cyclic quadrilateral?

Concept: Every angle of a cyclic quadrilateral is$\Rightarrow \angle CBE=\angle ADC=$ on a circle (circumscribed circle), and the sum of any two opposite angles of a cyclic quadrilateral is 180˚.

Here, $ABCD$ is a cyclic quadrilateral.

When one of the sides of cyclic quadrilateral is produced, then the exterior angle will be equal to the opposite interior angle. 

$\Rightarrow \angle CBE=\angle ADC={70}^{°}$

Since angle subtended by an arc of circle at the centre is twice the angle subtended by the arc on circumference,

$\angle AOC=2\angle ADC=2\times {70}^{°}={140}^{°}$

Hence, the value of $\angle AOC$ is ${140}^{°}$