Sign in
Please select an account to continue using cracku.in
↓ →
In the given figure, PQRS is a cyclic quadrilateral. What is the measure of the angle PQR if PQ is parallel to SR?
In the cyclic quadrilateral PQRS,
Sum of opposite angles = 180$$^{\circ\ }$$
$$=$$> $$\angle$$SPQ + $$\angle$$SRQ = 180$$^{\circ\ }$$
$$=$$> 110$$^{\circ\ }$$ + $$\angle$$SRQ = 180$$^{\circ\ }$$
$$=$$> $$\angle$$SRQ = 70$$^{\circ\ }$$
Given, PQ is parallel to SR
RQ is the transversal intersecting the parallel lines PQ and SR
Sum of the interior angles on the same side of the transversal is 180$$^{\circ\ }$$
$$=$$> $$\angle$$SRQ + $$\angle$$PQR = 180$$^{\circ\ }$$
$$=$$> 70$$^{\circ\ }$$ + $$\angle$$PQR = 180$$^{\circ\ }$$
$$=$$> $$\angle$$PQR = 110$$^{\circ\ }$$
Hence, the correct answer is Option A
Create a FREE account and get: