Question 12

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Jambmaths question: 

In the diagram above, O is the centre of the circle $\angle UOT=70^\circ$ and $\angle RST=100^\circ$ Calculate $\angle RUO$

Option A: 

50o

Option B: 

20o

Option C: 

80o

Option D: 

25o

Jamb Maths Solution: 

$\begin{align}  & R\overset{\wedge }{\mathop{U}}\,T+R\overset{\wedge }{\mathop{S}}\,T={{180}^{\circ }}\text{   } \\ & \text{ }\!\!\{\!\!\text{ sum of opp}\text{.}\angle \text{s of cyclic quad=18}{{\text{0}}^{o}}\} \\ & R\overset{\wedge }{\mathop{U}}\,T+100={{180}^{\circ }} \\ & R\overset{\wedge }{\mathop{U}}\,T={{80}^{\circ }} \\ & UO=OT\text{        }\!\!\{\!\!\text{ radius of circle }\!\!\}\!\!\text{ } \\ & O\overset{\wedge }{\mathop{U}}\,T=U\overset{\wedge }{\mathop{T}}\,O\text{    }\!\!\{\!\!\text{ Base angles of issoscele }\Delta \text{ }\!\!\}\!\!\text{ } \\ & a+a+{{70}^{\circ }}={{180}^{\circ }}\text{ }\!\!\{\!\!\text{ sum of angles in a }\Delta \text{ }\!\!\}\!\!\text{ } \\ & a={{55}^{\circ }} \\ & R\overset{\wedge }{\mathop{U}}\,T+R\overset{\wedge }{\mathop{U}}\,O={{80}^{\circ }} \\ & R\overset{\wedge }{\mathop{U}}\,T={{80}^{\circ }}-{{55}^{\circ }}={{25}^{\circ }} \\\end{align}$

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