O is the centre of the circle and <PQR = 110 degree. Then <OPR egual to :

(A) 55 degree

(B) 20degree

(C) 40 degree

(D) 70 degree

Please answer fast. :(

We know that, the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.

∴ Reflex ∠ROP = 2 × ∠PQR

⇒ Reflex ∠ROP = 2 × 110° = 220°

⇒ ∠ROP = 360° – Reflex ∠ROP = 360° – 220° = 140°

In ΔROP,

OP = OR         (Radius of the circle)

⇒ ∠ORP = ∠OPR      (Equal sides have equal angles opposite to them)

∠ORP + ∠OPR + ∠ROP = 180°        (Angle sum property)

∴ 2∠OPR  + 140° = 180°

⇒ 2∠OPR = 180° – 140°

⇒ 2∠OPR = 40°

⇒ ∠OPR = 20°

Thus, the measure of ∠OPR is 20°.