Question

Draw any polygon and divide it into triangular parts as shown here. Thus work out the sum of the measures of the angles of the polygon.

Answer 1

As the sum of the angle of a triangle is 180^∘.
Therefore, h + g + f = 180^∘ ...(1)
i + e + a = 180^∘ ...(2)
b + c + d = 180^∘ ...(3)
Add (1), (2) and (3)
h + g + f + i + e + a + b + c + d = 180^∘ + 180^∘ + 180^∘
⇒ h + i + g + f + e + d + b + c = 540^∘
⇒ E + D + C + B + A = 540^∘
Therefore, the sum of the angles of a pentagon is 540^∘