UPSC 2015 CDS I Math Paper

AP and BP are tangents to the circle
∴ ∠OAP = ∠OBP =90° (Radiusis perpendicular to the tangent at the point of contact)
In quadrilateral OAPB,
130° + 90° + 90° + ∠APB = 360°
⇒ ∠APB = 360°-310°
⇒ ∠APB = 50°