JEE Mains · Maths · STD 11 - 8. sequence and series
The interior angles of a polygon with n sides, are in an A.P. with common difference \(6^{\circ}\). If the largest interior angle of the polygon is \(219^{\circ}\), then n is equal to
- A 10
- B 20
- C 30
- D 40
Answer & Solution
Correct Answer
(B) 20
Step-by-step Solution
Detailed explanation
\(\frac{n}{2}[2 a+(n-1) 6]=(n-2) 180^{\circ}\) and \(a n+3 n^2-3 n=3 n(n-2) 180^{\circ}\)...(i) \(\begin{aligned} & \therefore \quad \text { Given } a+(n-1) 6^{\circ}=219^{\circ} \\ & \Rightarrow a=225^{\circ}-6 n^{\circ} \end{aligned}\) Putting value of \(a\) in (i)…
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