Question 44

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waecmaths question: 

In the diagram , O is the centre of the circle. Find the value of x

Option A: 

34o

Option B: 

29o

Option C: 

17o

Option D: 

14o

waecmaths solution: 

\[\begin{align}  & \angle POR={{56}^{\circ }} \\ & \angle ROQ={{180}^{\circ }}-\angle POR \\ & \angle ROQ={{180}^{\circ }}-{{56}^{\circ }}={{124}^{\circ }} \\ & \left| RO \right|=\left| OQ \right|\text{   }\!\!\{\!\!\text{ radius of circle }\!\!\}\!\!\text{ } \\ & \angle ORQ=\angle OQR=2{{x}^{\circ }}\text{  }\!\!\{\!\!\text{ base }\angle s\text{ of Isso }\vartriangle \} \\ & \angle ROQ+\angle ORQ+\angle OQR={{180}^{\circ }}\text{ } \\ & \text{ }\!\!\{\!\!\text{ sum of }\angle s\text{ in a }\vartriangle \} \\ & {{124}^{\circ }}+2{{x}^{\circ }}+2{{x}^{\circ }}={{180}^{\circ }} \\ & 4{{x}^{\circ }}={{56}^{\circ }} \\ & x={{14}^{\circ }} \\\end{align}\]Alternatively method\[\begin{align}  & \angle ORQ+\angle OQR=\angle POR \\ & \{sum\text{ o}f\text{ two opp int }\angle s=\angle \text{ of a }\vartriangle \} \\ & 2x+2x={{56}^{\circ }} \\ & x={{14}^{\circ }} \\\end{align}\]

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