In a regular polygon, the number of
In a regular polygon, the number of diagonals is 9. Find the difference between one interior angle and one exterior angle of the polygon.
एक समबहुभुज में विकर्णों की संख्या 9 है। बहुभुज के एक अंतः कोण और एक बाह्य कोण के बीच का अंतर ज्ञात कीजिए।
Detailed Solution & Logic
Correct Answer:
\(60^\circ\)
Number of diagonals D = 9
$ D = \frac{n(n-3)}{2} $
$ 9 = \frac{n(n-3)}{2} $
18 = n(n-3)
$ n^2 - 3n - 18 = 0 $
n = 6
Interior angle $ = \frac{(n-2) \cdot 180}{n} = \frac{4 \cdot 180}{6} = 120^\circ $
Exterior angle $ = 180 - 120 = 60^\circ $
Difference $ = 120 - 60 = 60^\circ $
Answer: $60^\circ$
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