Answer is B. 134°
Given:
∠QPR = 46°
Property 1: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.
Property 2: Sum of all angles of a quadrilateral = 360°.
By property 1, ∆OQP is right-angled at ∠OQP (i.e., ∠OQP = 90°) and ∆ORP is right-angled at ∠ORP (i.e., ∠ORP = 90°).
Now by property 2,
∠OQP + ∠ORP + ∠QOR + ∠QPR = 360°
⇒ ∠QOR = 360° - (∠OQP + ∠ORP + ∠QPR)
⇒ ∠ROP = 360° - (90° + 90° + 46°)
⇒ ∠ROP = 360° - 226°
⇒ ∠ROP = 134°
Hence, ∠ROP = 134°
