Question 5

loading...

Prev/Next links

waecmaths question: 

In the diagram OP and OR are radii, \[\left| PQ \right|=\left| QR \right|\] and reflex $\angle POR$ is 240o. Calculate the value of x

Option A: 

60o

Option B: 

55o

Option C: 

50o

Option D: 

45o

waecmaths solution: 

\[\begin{align}  & \angle PQR=\tfrac{1}{2}{{(\angle POR)}_{reflex}}=\tfrac{1}{2}({{240}^{\circ }})={{120}^{\circ }} \\ & \{\angle \text{ at circumference }=\tfrac{1}{2}\angle \text{ at centre }\!\!\}\!\!\text{ } \\ & \angle QPR=\angle QRP=a\text{  }\!\!\{\!\!\text{  base }\angle s\text{ of issoceles }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & a+a+{{120}^{\circ }}={{180}^{\circ }} \\ & a=\angle QPR={{30}^{\circ }} \\ & \angle POR={{360}^{\circ }}-{{240}^{\circ }}={{120}^{\circ }}\text{   }\!\!\{\!\!\text{ }\angle s\text{ at a point }\!\!\}\!\!\text{ } \\ & \left| PO \right|=\left| RO \right|\text{   }\!\!\{\!\!\text{ radius of a circle }\!\!\}\!\!\text{ } \\ & \angle OPR=\angle PRQ\text{  }\!\!\{\!\!\text{  base }\angle s\text{ of issoceles }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & \angle OPR=\angle PRQ=b \\ & b+b+\angle PO{{R}_{internal}}={{180}^{\circ }} \\ & 2b+{{120}^{\circ }}={{180}^{\circ }} \\ & b={{30}^{\circ }} \\ & x=a+b={{30}^{\circ }}+{{30}^{\circ }}={{60}^{\circ }} \\\end{align}\]

maths year: 
maths topics: