Question

a polygon has five diaganols then the number of sides in the polygins. a)5. b)3 c)6 d) 4​

Answer 1

Step-by-step explanation:

option b 3

Answer 2

Answer:

↣5

Step-by-step explanation:

We know that,

↣Number of diagonals of a polygon=

$\frac{n(n - 3)}{2}$

↣According to the question,

$↣ \frac{n(n - 3)}{2} = 5 \\ ↣n(n - 3) = 10 \\ ↣ {n}^{2} - 3n = 10 \\ ↣ {n}^{2} - 3n - 10 = 0 \\ ↣ {n}^{2} + 2n - 5n - 10 \\ ↣n(n + 2) - 5(n + 2) \\↣( n - 5)(n + 2)$

$↣n - 5 = 0 \\↣ n = 5$

OR,

$↣n + 2 = 0 \\↣ n = - 2$

↣Neglected, because the side of polygon can't be negative.

Hence,

↣ n = 5

↣The side of polygon are 5.

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