Question

In the given figure below, $AD$ is a diameter. $O$ is the centre of the circle. $AD$ is parallel to $BC$ and $\angle CBD={32}^{\circ }$. Find $\angle AOB$ (in ${}^{\circ }$)

Answer 1

Given: $AD\parallel BC$
$\therefore \angle ADB=\angle DBC={32}^{\circ }$ (alternate angles)
$\because OB=OD$ (radii of the circle)
$\angle AOB=2\angle ODB$ (angle at the centre is twice the angle at remaining circumference)
$=2\times 32={64}^{\circ }$