BECE Mathematics 2020 Paper

Concept:An isosceles triangle has two equal sides, so the base angles opposite them are equal.Angles on a straight line add up to $180^\circ$.Solution:The two sides marked with a dash are equal, so the two base angles of the triangle are equal.The base angle on the right is $56^\circ$, so the base angle on the left (inside the triangle) is also $56^\circ$.The angle $x$ lies outside the triangle, on the straight base line next to this $56^\circ$ angle. Angles on a straight line add up to $180^\circ$:$x + 56^\circ = 180^\circ$$x = 180^\circ - 56^\circ = 124^\circ$Key point: $x$ is an exterior angle, not the base angle itself, so the answer is not $56^\circ$.Answer:Option D ($124^\circ$)