Question 37

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waecmaths question: 

     In the diagram, PQRST is a regular polygon with the sides of OR and TS produced to meet at V. Find the size of $\angle RVS$

Option A: 

36o

Option B: 

54o

Option C: 

60o

Option D: 

72o

waecmaths solution: 

The given polygon is a pentagon (5 sides)\[\begin{align}  & Sum\text{ of angle}=(n-2){{180}^{\circ }}=(5-3){{180}^{\circ }}={{540}^{\circ }} \\ & \text{Each angle in the pentagon will be }\frac{{{540}^{\circ }}}{5}={{108}^{\circ }} \\ & \angle TSR={{108}^{\circ }} \\ & \angle TSR+\angle RSV={{180}^{\circ }} \\ & \angle RSV={{180}^{\circ }}-{{108}^{\circ }}={{72}^{\circ }} \\ & \angle QRS={{108}^{\circ }} \\ & \angle QRS+\angle SRV={{180}^{\circ }} \\ & \angle SRV={{180}^{\circ }}-{{108}^{\circ }}={{72}^{\circ }} \\ & \angle RVS+\angle SRV+\angle RSV={{180}^{\circ }}\text{    }\!\!\{\!\!\text{ Sum of angles in a triangle }\!\!\}\!\!\text{ } \\ & \angle RVS+{{72}^{\circ }}+{{72}^{\circ }}={{180}^{\circ }} \\ & \angle RVS={{36}^{\circ }} \\\end{align}\]

maths year: