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In the diagram, PQRST is a regular polygon with sides QR and TS produced to...

Mathematics
WAEC 2013

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
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Correct Answer: Option A
Explanation
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

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