BECE Mathematics 2021 Paper

PropertiesAlternate AnglesAlternate angles are equalFrom the diagram above, angle $D C B$ and angle $O B A$ are alternate anglesHence angle $D C B=O B A$ Sum of angles in triangleSum of angles in a triangle add up to $180^{\circ}$$A^{\circ}+B^{\circ}+C^{\circ}=180^{\circ}$From the diagram in the question, angle $x^{\circ}+$ angle $O B A+$ angle $B A O=180^{\circ}$ (Sum of angles in triangle)$\;x^{\circ}+O B A^{\circ}+20^{\circ}=180^{\circ}$$\;x^{\circ}=180^{\circ}-20^{\circ}-O B A^{\circ}$$\;x^{\circ}=160^{\circ}-O B A^{\circ}$ Sum of angles on a straight line$x+y=180$ (sum of angles on a straight line add up to 180)From the diagram in the question, $120+$ angle DCB = 180 (Sum of angles on a straight line)$\;120+D C B=180$$\;D C B=180-120$$\;D C B=60$ Angle $D C B=O B A$, alternate anglesIf angle $D C B=60$, then angle $O B A$ is also 60From $x^{\circ}=160^{\circ}-O B A^{\circ}$$O B A=60$$\;x=160-60$$\;x=100$