In the diagram, PQRST is a regular polygon with the sides of OR and TS produced to meet at V. Find the size of $\angle RVS$
36o
54o
60o
72o
The given polygon is a pentagon (5 sides)\[\begin{align} & Sum\text{ of angle}=(n-2){{180}^{\circ }}=(5-3){{180}^{\circ }}={{540}^{\circ }} \\ & \text{Each angle in the pentagon will be }\frac{{{540}^{\circ }}}{5}={{108}^{\circ }} \\ & \angle TSR={{108}^{\circ }} \\ & \angle TSR+\angle RSV={{180}^{\circ }} \\ & \angle RSV={{180}^{\circ }}-{{108}^{\circ }}={{72}^{\circ }} \\ & \angle QRS={{108}^{\circ }} \\ & \angle QRS+\angle SRV={{180}^{\circ }} \\ & \angle SRV={{180}^{\circ }}-{{108}^{\circ }}={{72}^{\circ }} \\ & \angle RVS+\angle SRV+\angle RSV={{180}^{\circ }}\text{ }\!\!\{\!\!\text{ Sum of angles in a triangle }\!\!\}\!\!\text{ } \\ & \angle RVS+{{72}^{\circ }}+{{72}^{\circ }}={{180}^{\circ }} \\ & \angle RVS={{36}^{\circ }} \\\end{align}\]
