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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