BECE Mathematics 2017 Paper

Concept:Isosceles triangles have two equal sides and two equal base angles.Explanation:In $\triangle UVW$, the equal sides are $UV$ and $UW$.The angle between these equal sides is $\angle VUW = 70^{\circ}$.The base is $VW$, so the base angles are $\angle UVW$ and $\angle UWV$.In an isosceles triangle, the base angles are equal:$\angle UVW = \angle UWV$.Let $\angle UVW = \angle UWV = x$.The sum of angles in any triangle is $180^{\circ}$.So, $x + x + 70^{\circ} = 180^{\circ}$.Simplify: $2x + 70^{\circ} = 180^{\circ}$.Subtract $70^{\circ}$ from both sides: $2x = 110^{\circ}$.Divide both sides by $2$: $x = 55^{\circ}$.Therefore, $\angle UVW = 55^{\circ}$.Answer:$\angle UVW = 55^{\circ}$, which matches option C.