Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle…

PA and PB are tangents from the external point P to the circle with centre O.
Correct figure
$\angle OAP = \angle OBP = 90^\circ$
In quadrilateral OAPB,
$\angle APB + \angle OAP + \angle OBP + \angle AOB = 360^\circ$
$\Rightarrow \angle APB + 90^\circ + 90^\circ + \angle AOB = 360^\circ$
$\Rightarrow \angle APB + \angle AOB = 180^\circ$
$\therefore \angle APB$ and $\angle AOB$ are supplementary.