Question 9

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waecmaths question: 

In the diagram $KL\parallel MN,\angle NMP={{30}^{\circ }}$ and $\angle NMP={{45}^{\circ }}$ find the size of the reflex $\angle KPM$

Option A: 

285o

Option B: 

255o

Option C: 

225o

Option D: 

210o

waecmaths solution: 

 $\begin{align} &\text{ Draw a line AB passing through point P parallel to KL and MN} \\ & \angle APK=\angle LKP={{30}^{\circ }}\text{   }\!\!\{\!\!\text{ Alternate angles} \\ & \angle APM=\angle NMP={{45}^{\circ }}\text{   }\!\!\{\!\!\text{ alternate angles }\!\!\}\!\!\text{ } \\ & \angle KPM={{30}^{\circ }}+{{45}^{\circ }}={{75}^{\circ }} \\ & \angle KP{{M}_{reflex}}={{360}^{\circ }}-{{75}^{\circ }}={{285}^{\circ }} \\\end{align}$

maths year: