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

Given: $\angle CBE={70}^o$

Here, $ABCD$ is a cyclic quadrilateral.

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

$\therefore \angle CBE=\angle ADC={70}^o$

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

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

Hence, the value of $\angle AOC$ is ${\mathbf{140}}^{\mathbf{o}}$.