Answer:
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
