Question

If the sum of the interior angles except one angle of convex polygon has 2100° the number of sides of the polygon is /are

Answer 1

In the above Question , the following information is given -

The sum of the interior angles except one angle of convex polygon has 2100° .

To find -

The number of sides of a polygon are -

Solution -

Here,

The sum of the interior angles except one angle of convex polygon has 2100° .

Let us assume that this polygon has a n number of sides .

So ,

Sum of all angles -

=> ( n - 2 ) × 180°

Now ,

This is equal to 2100 ° + Excluded angle

So,

180n - 360 = 2100 + Excluded angle

=> 180 n = 2460 ° + Excluded angle .

So ,

n = [ 2460 ° + Excluded angle ] / 180°

Now ,

We have the following conditions .

1. N is an integer .

2. Excluded angle can have a minimum value of 0° and a maximum value of 180°

Case 1 -

Excluded Angle = 0 °

n = [ 2460 ° / 180° ]

=> n = 13.6667

Case 2 -

Excluded Angle = 180°

n = [ 2640 ° / 180 ° ]

=> n = 14.6667

But , n is an integer .

So , the only possible value of n is 14

Thus , this polygon has 14 sides .

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Answer 2

GIVEN:

• Sum of interior angles excepts one angle of a convex polygon = 2100°

TO FIND:

• No. of sides of the polygon

SOLUTION:

We know that

Sum of angles in a polygon

→ (n - 2) × 180°

Where , n : no. of sides of the polygon

Given ,

2100° + excluded angle

So,

180n - 360 = 2100 + Excluded angle

180n = 2460° + excluded angle

n = (2460° + excluded angle)/180

Condition: Excluded angle have 0° - 180°

Where, excluded angle = 0°

n = 2460°/180°

n = 13.66 ≠ integer

_________________________

Where , excluded angle = 180°

n = 2460° + 180°/180°

n = 14.667 ≈ 14 ≈ integer

Hence, the polygon is 14 sided