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