Question 32

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waecmaths question: 

In the figure, PQ is a tangent to the circle at R and UT is parallel to PQ if $\angle TRQ={{x}^{\circ }}$. Find $\angle URT$in terms of x

Option A: 

2x

Option B: 

(90 – x)o

Option C: 

(90 + x)o

Option D: 

(180 – 2x)o

waecmaths solution: 

 $\begin{align}  & \angle RUT=\angle SRQ\text{    }\!\!\{\!\!\text{ alternate angles }\!\!\}\!\!\text{ } \\ & \angle UTR=\angle SRQ\text{    }\!\!\{\!\!\text{ Alternate segment }\!\!\}\!\!\text{ } \\ & \angle URT={{180}^{\circ }}-(\angle RUT+\angle UTR)={{180}^{\circ }}-({{x}^{\circ }}+{{x}^{\circ }}) \\ & \angle URT={{180}^{\circ }}-2x \\\end{align}$

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