If PQ and PR are the two tangents to a circle with center O, and ∠QOR= $150^\circ$, then ∠QPR is equal to:

Solution / समाधान:
PQ and PR are tangents, so
$OQ \perp PQ$ and $OR \perp PR$
In quadrilateral OQPR:
$\angle OQP = 90^\circ$ and $\angle ORP = 90^\circ$

Sum of all angles in quadrilateral = $360^\circ$

So,
$\angle QOR + \angle QPR + 90^\circ + 90^\circ = 360^\circ$

$\angle QOR + \angle QPR + 180^\circ = 360^\circ$

$\angle QPR = 360^\circ - 180^\circ - 150^\circ = 30^\circ$

Final Answer / अंतिम उत्तर: $30^\circ$