In the diagram, PQRST is a regular polygon with sides QR and TS produced to meet at V. Find the size of < RVS

In the diagram, PQRST is a regular polygon with sides QR and TS produced to meet at V. Find the size of < RVS

A.

36o

B.

54o

C.

60o

D.

72o

Correct answer is A

PQRST is a regular polygon with 5 sides-pentagon n = 5, Each exterior angle = \(\frac{360^o}{n}\)

= \(\frac{350}{5}\) = 70o

Each interior angle = 180 - 72o

(< s on str. line) = 180o

Since the pentagon is regular, the exterior angles are equal < R = 72o and < S = 72o

< RVS = 180o - (< R + < S)

= 180o - (72o + 72o)

= 180o - 144o

= 36o