Question 23

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waecmaths question: 

In the diagram, O is the centre of the circle, $OM\parallel XZ$and $\angle ZOM={{25}^{\circ }}$. Calculate $\angle XYZ$

Option A: 

50o

Option B: 

55o

Option C: 

60o

Option D: 

65o

waecmaths solution: 

Construction: Join point O and X together to produce OX\[\begin{align}  & OZ=OX\text{   }\{Radius\text{ }of\text{ }circle\} \\ & \angle XZM=\angle ZOM={{25}^{\circ }}\text{   }\!\!\{\!\!\text{ alternate angles }\!\!\}\!\!\text{ } \\ & \angle OZX=\angle OXZ\text{  }\!\!\{\!\!\text{ Base }\angle s\text{ of Isso }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & \angle ZOX={{180}^{\circ }}-\angle OZX-\angle OXZ\text{  }\!\!\{\!\!\text{ }\angle \text{s in a }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & \angle ZOX={{180}^{\circ }}-{{25}^{\circ }}-{{25}^{\circ }}={{130}^{\circ }} \\ & \angle XYZ=\tfrac{1}{2}\angle ZOX\text{   }\!\!\{\!\!\text{ }\angle \text{ at circumference}=\tfrac{1}{2}\times \angle \text{ at centre }\!\!\}\!\!\text{ } \\ & \angle XYZ=\tfrac{1}{2}({{130}^{\circ }})={{65}^{\circ }} \\\end{align}\]

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