Question 23

loading...

Prev/Next links

waecmaths question: 

In the diagram $MN\parallel OP,\angle NMQ={{65}^{\circ }}$ and $\angle QOP={{125}^{\circ }}$ what is the size of $\angle MQR$? 

Option A: 

110o

Option B: 

120o

Option C: 

130o

Option D: 

160o

waecmaths solution: 

$\begin{align}  & \angle QOP={{125}^{\circ }} \\ & \angle PON={{180}^{\circ }}-{{125}^{\circ }}={{55}^{\circ }}\text{ } \\ & \text{ }\!\!\{\!\!\text{ }\angle s\text{ on a straight line }\!\!\}\!\!\text{ } \\ & \angle MNO=\angle PON={{65}^{\circ }}\text{  }\!\!\{\!\!\text{ alternate angles }\!\!\}\!\!\text{ } \\ & \text{In }\vartriangle MNQ \\ & \angle QMN+\angle MNQ+\angle MQN={{180}^{\circ }} \\ & {{65}^{\circ }}+{{55}^{\circ }}+\angle MQN={{180}^{\circ }} \\ & \angle MQN={{60}^{\circ }} \\ & \angle MQN+\angle MQR={{180}^{\circ }} \\ & \angle MQR={{180}^{\circ }}-{{60}^{\circ }}={{120}^{\circ }} \\\end{align}$

maths year: