BECE Mathematics 2019 Paper

Concept:When two parallel lines are cut by a transversal, vertically opposite angles and alternate interior angles are equal, and angles on a straight line add to $180^\circ$.Explanation:Given $MN \parallel TU$ and transversal $TS$ intersects $MN$ at $O$.Also, $\angle MOS = 115^\circ$.$\angle NOT$ is vertically opposite to $\angle MOS$.Therefore, $\angle NOT = 115^\circ$.$\angle MOT$ and $\angle NOT$ lie on a straight line at $O$.So, $\angle MOT + \angle NOT = 180^\circ$.Thus, $\angle MOT = 180^\circ - 115^\circ = 65^\circ$.Since $MN \parallel TU$, alternate interior angles are equal.Hence, $\angle MOT = \angle OTU$.Therefore, $\angle OTU = 65^\circ$.Answer:$\angle OTU = 65^\circ$, so the correct option is A.