waecmaths question:
In the diagram, O is the centre of the circle, $\angle SQR={{60}^{{}^\circ }},\angle SPR=y$ and $\angle SOR=3x$ find the value of (x + y)
Option A:
110o
Option B:
100o
Option C:
80o
Option D:
70o
waecmaths solution:
\[\begin{align} & y=\angle SQR={{60}^{\circ }}\text{ }\!\!\{\!\!\text{ Angle in the same segment }\!\!\}\!\!\text{ } \\ & \angle SOR=2\times \angle SQR\text{ }\!\!\{\!\!\text{ }\angle \text{at centre}=2\times \angle \text{ at circf }\!\!\}\!\!\text{ } \\ & 3x=2\times {{60}^{\circ }}={{120}^{\circ }} \\ & x={{40}^{\circ }} \\ & x+y={{40}^{\circ }}+{{60}^{\circ }}={{100}^{\circ }} \\\end{align}\]
maths year:
maths topics: