Polygonal Angles 2 – 10-gon Angles

if join all angel with center then 10 triangle will create. Sum of 10 triangle's angles is 180*10=1800, avoid 360 of center then we get 1800-360=1440.

when sum of internal angle is asked for any of the regular polygon we can use the formula which is as under, 180 X (n-2)............where n is the number of sides of a polygon, hence, 180 X (10-2)=180 X 8 = 1440

Now keeping in mind that the sum of all angles in a triangle = 180. and rectangle = 360, so the increasing number of sides means adding 180 to it. So, 360 +180 +180+180+180+180+180 = 1440 degrees Bingoo :)

I know the formulae is n -2 * 180 but i find the first method more interesting and conceptual

The total interior angle of a decagon is given by, Total interior angle = (n - 2)180 degrees. So, in a decagon the sum of all interior angle = 1440 degrees. Since the sides are equal, the interior angle at each vertex is = = 144 degrees. For any polygon, the total exterior angle is 360 degrees.

The sum of the interior angles of a triangle = (nx180)-360 = 2160-360 =1440

Using the formula for the sum of the angles in a regular polygon:

$\large \color{#3D99F6} (n - 2)180 = \text {Sum of angles in a polygon}$

where $n$ is the number of sides...

$\therefore \text {(10 - 2) * 180 = 8 * 180 = 1440 degrees}$ $\large \color{#D61F06} =1440$

It's called a decagon, by the way.

The sum of the internal angles for a polygon of $n$ sides is $180(n-2)$ . Solving this for $n=10$ , we find that the sum comes to $\boxed{1440^{\circ}}$ .

(n-2)180 where n is the amount of sides. So: (10-2)(180)=1440

we can find any internal angle of polygon by the formula 180(n-2) where n is no. of sides

for any polygon the sum of the interior angles is 180 (n-2), n being the number of sides. here n is 10 so 180 (10-2) i.e. 180*8=1440

180(n-2) for n sided polygen and it has 10 sides so n=10 then applying the above formulae, 180(10-2) = 180*8 = 1440 answer

there r 10 sides. w.k.t sum of the interior angles is 180(n-2) =>180(10-2) 180(8) 1440

=180(n-2) =180(10-2) =180x8 =1440