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