Questio 15

loading...

Prev/Next links

waecmaths question: 

In the diagram, $\angle QPT=\angle PTS={{90}^{\circ }}$, $\angle PQR={{110}^{\circ }}$and . Find the size of the obtuse angle QRS

Option A: 

140o

Option B: 

130o

Option C: 

120o

Option D: 

110o

waecmaths solution: 

$\begin{align}  & \text{Produce }\left| SR \right|\text{ to the point }A\text{ on line }\left| PT \right| \\ & \text{In }\vartriangle ATS \\ & \angle TAS+\angle ATS+\angle TSA={{180}^{\circ }} \\ & \angle TAS+{{90}^{\circ }}+{{20}^{\circ }}={{180}^{\circ }} \\ & \angle TAS={{70}^{\circ }} \\ & \angle PTR={{180}^{\circ }}-{{70}^{\circ }}\text{    }\!\!\{\!\!\text{ }\angle \text{s on the straight line }\!\!\}\!\!\text{ } \\ & \angle PTR={{110}^{\circ }} \\ & \text{Consider the quadrilateral }APQR \\ & {{110}^{\circ }}+{{90}^{\circ }}+{{110}^{\circ }}+\angle ARQ={{360}^{\circ }} \\ & \angle ARQ={{50}^{\circ }} \\ & \angle ARQ+\angle QRS={{180}^{\circ }}\text{    }\!\!\{\!\!\text{ }\angle s\text{ on a straight line }\!\!\}\!\!\text{ } \\ & \text{5}{{\text{0}}^{\circ }}+\angle QRS={{180}^{\circ }} \\ & \angle QRS={{130}^{\circ }} \\\end{align}$

maths year: