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CBSE Class 7 Answered

In a regular polygon the ratio of the inner and outer angle is 7:2; What is the each angle?How many sides does the polygon have
Asked by Nimmi | 19 Jan, 2019, 01:25: AM
answered-by-expert Expert Answer
Ratio of inner angle to outer angle = 7 : 2
 
Let inner angle be 7x and outer angle be 2x.
sum of inner anf outer angles = 7x + 2x = 9x = 180  or   x = 20
 
Hence inner angle = 7×20 = 140°
 
sum of interior angles of regular polygon of n sides = (n-2)×180
 
measure of each angle = begin mathsize 12px style fraction numerator n minus 2 over denominator n end fraction cross times 180 space equals space 140 end style
From the above eqn. we get n = 9
Answered by Thiyagarajan K | 19 Jan, 2019, 08:26: AM
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