Points A and B are on a circle with centre O. PAM and PBN are tangents to the circle at A and B respectively from a point P outside the circle. Point Q is on the major arc AB such that ∠QAM = 58° and ∠QBN = 50°, then find the measure (in degrees) of ∠APB.

From point P outside the circle, PA and PB are tangents. PA = PB and OA ⟂ PA, OB ⟂ PB (tangent ⟂ radius). Given ∠QAM = 58° and ∠QBN = 50°, we need to find ∠APB. Since PA is tangent at A and QA passes through A, ∠QAM includes angle between QA and tangent PA. Using tangent properties and angle calculations, ∠APB = 36°. Note: This requires the diagram showing point positions.