What is the formula for interior angle sum

S = (n - 2) * 180. It is also possible to calculate the measure of each angle if the polygon is regular by dividing the sum by the number of sides.

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Step-by-step explanation:

The sum of an interior angle of a regular polygon varies and it is given by the formula

θ = (n-2) * 180°

Where,

θ is the sum of angle in the polygon

n is the total sides of the polygon.

Let analyze some shapes

1. Triangle

A triangle has 3 sides and 3 angles

Then, n=3

So, θ = (n-2) * 180°

θ = (3-2) * 180°

θ=1*180°

θ=180°

So, that is why the sum of angle in a triangle is 180°

2. Decagon,

Decagon has 10 sides

n=10

θ = (10-2) * 180°

θ = 8*180°

θ=1440°

Sum of angle in a decagon is 1440°

You can try all this

n=4. quadrilateral

n=5. Pentagon

n=6. Hexagon

n=7. Heptagon

n=8. Octagon

n=9 Nonagon