Question 33

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waecmaths question: 

In the diagram, $\overline{OT}$and $\overline{PR}$ are straight lines $\angle ROS=(3n-{{20}^{\circ }}),$$\angle POT=2m$, $\angle SOT=n$$\angle POL=m$ and $\angle QOL$is a right angle. Find the value of n

waecmaths solution: 

$\begin{align}  & Consider\text{ }\vartriangle QTP \\ & m+2m+{{90}^{\circ }}={{180}^{\circ }} \\ & m={{30}^{\circ }} \\ & \text{Consider }PORS \\ & 2m+n+3n-{{20}^{\circ }}={{180}^{\circ }} \\ & 2({{30}^{\circ }})+n+3n-20={{180}^{\circ }} \\ & {{60}^{\circ }}+4n-{{20}^{\circ }}={{180}^{\circ }} \\ & 4n={{140}^{\circ }} \\ & n={{35}^{\circ }} \\\end{align}$

maths year: