BECE Mathematics 2020 Paper

Concept:An isosceles triangle is a triangle that has two equal sides. In any isosceles triangle, the angles opposite the equal sides are equal; these are called the base angles.Explanation:The given triangle is isosceles because two of its sides are equal.So the base angles are equal.From the diagram, one base angle is $56^\circ$.Hence, the other base angle is also $56^\circ$.The marked angle is $y$, and it is the third angle of the triangle.For any triangle, the sum of all interior angles is always $180^\circ$.So we write the equation:$$y + 56^\circ + 56^\circ = 180^\circ$$Adding the base angles gives:$$y + 112^\circ = 180^\circ$$Subtract $112^\circ$ from both sides:$$y = 180^\circ - 112^\circ$$$$y = 68^\circ$$Answer:$y = 68^\circ$, so the correct option is A.