Math, asked by kerandsangma7898, 5 months ago

the number of sides of an n-gon if the sum of the interior angle is 1800°​

Answers

Answered by hanockgamer611
5

Answer:

The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n – 2), where n is the number of sides. The problem concerns a polygon with twelve sides, so we will let n = 12. The sum of the interior angles in this polygon would be 180(12 – 2) = 180(10) = 1800.

Answered by itzHATERxx
0

Answer:

The sum of exterior angle and its adjacent interior is 180

0

, that is,

e+i=180

0

Since each exterior angle is equal to twice its adjacent interior angle, therefore, substitute 2i=e or i=

2

e

.

e+

2

e

=180

0

2

2e+e

=180

0

2

3e

=180

0

⇒3e=180

0

×2

⇒3e=360

0

⇒e=

3

360

0

=120

0

We know that the measure of exterior angle is e=(

n

360

)

0

where n is the number of sides.

Here, it is given that the exterior angle is e=120

0

, therefore,

n=

e

360

=

120

360

=3

Hence, the number of sides is 3

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