BECE Mathematics 2012 Paper

Concept: When two parallel lines are cut by a transversal, alternate interior angles are equal, and angles on a straight line add to $180^\circ$.Explanation:Let the angle vertically opposite or corresponding to the given $35^\circ$ be $b$.Since $PQ \parallel RS$ and $UV$ is the transversal, angle $b = 35^\circ$ by alternate angles.Now, angle $a$ and angle $b$ lie on the same straight line, so they are supplementary.Thus, $a + b = 180^\circ$.Substitute $b = 35^\circ$: $a + 35^\circ = 180^\circ$.So, $a = 180^\circ - 35^\circ = 145^\circ$.Answer: $a = 145^\circ$, which is option D.