BECE Mathematics 2017 Paper

Concept:Use parallel line alternate angles, the isosceles triangle property, and the angle-sum rule for triangles.Explanation:In the diagram, $AB \parallel DE$, and $BD$ is a transversal. Therefore, alternate angles are equal:$\angle ABD = \angle BDE$.Since $|BD| = |BE|$, $\triangle BDE$ is isosceles, so the base angles are equal:$\angle BDE = \angle BED$.The angles on the straight line at $B$ add up to $180^\circ$:$\angle ABD + 2x + 56^\circ = 180^\circ$.So,$\angle ABD = 180^\circ - 56^\circ - 2x = 124^\circ - 2x$.Thus, each base angle of $\triangle BDE$ is also $124^\circ - 2x$.Now apply the angle sum of a triangle to $\triangle BDE$:$2x + (124^\circ - 2x) + (124^\circ - 2x) = 180^\circ$.Simplify:$248^\circ - 2x = 180^\circ$.Therefore,$2x = 68^\circ$.$x = 34^\circ$.Answer:$x = 34^{\circ}$, so the correct option is C.