Question

The sum of the interior angles of a convex n-sided polygon is less than 2019°. The
maximum possible value of n is?​

Answer 1

Answer:

Each interior angle of the polygon is 108 degrees, so each exterior angle of the polygon is 180-108 = 72 degrees. So the number of sides is 360/72 = 5. Hence it is a regular pentagon.

Answer 2

Answer:

The maximum possible value of n is 13.

Step-by-step explanation:

Given,

sum of the interior angles of a convex n-sided polygon is less than 2019°.

Here we want to find maximum value of n.

But for solving this question,we need to know rule of sum of interior angles of a convex n-sided polygon.

We know,

If n is the number of sides of the polygon,then sum of interior angles is $(2n - 4) \times {90}^{o}$

By one example we can understand this concept more easily,

If some of interior angles is 900° then

$(2n - 4) \times {90}^{0} = {900}^{o} \\ (2n - 4) = \frac{ {900}^{o} }{ 90} \\ 2n - 4 = {10}^{o} \\ 2n = 10 - 4 \\ 2n = 6 \\ n = \frac{6}{2} \\ n = 3$

Here given sum is 2019°

Then,

$(2n - 4) \times {90}^{0} = {2019}^{o} \\ 2n - 4 = \frac{ {2019}^{o} }{ {90}^{o} } \\ 2n - 4 = 22.43 \\ 2n = 22.43 + 4 \\ 2n = 26.43 \\ n = \frac{26.43}{2} \\ n = 13.215 \\ n = 13 \: (approx)$

This is a problem of Geometry,

know more about Geometry:

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