BECE Mathematics 2022 Paper

You have to use the property of alternate angles of parallel linesAlternate angles are equal:Sometimes called $Z$ anglesWe can often spot interior alternate angles by drawing a $Z$ shapeFrom the diagram above, angle $A B C=$ angle $C D E=x$ (Alternate angles)Angle $B A C=y=D E C$ (Alternate angles)Angle $A B C=$ angle $C D E=x$ (Alternate angles)Angle $A B C=81^{\circ}, \therefore x=81^{\circ}$Since we know the angles $D C E$ and $C D E$, we can calculate the angle $D E C$ using the concept that angles in a triangle add up to $180^{\circ}$$x=81^{\circ} \; \text{ and } \; D C E=20^{\circ}$ Sum of angles in triangle add up to $180^{\circ}$$\;81+20+\; \text{ angle } \; D E C=180$$\;101+D E C=180$$\;D E C=180-101$$\;D E C=79$Since $B A C=y=D E C, y=79^{\circ}$