Question

in a pentagon two angles are 40 degree and 60 degree and the rest are in ratio 1 : 3 : 7 find the biggest angle of the Pentagon . ANS : 280°

Answer 1

60°+40°+x+3x+7x=540
100°+11x=540
11x=540°-100°
11x=440°
x=40°

x=40°,3x=120° and 7x=280°

Answer 2

Here Two Angles Given 40° and 60°

Let other 3 angles are x, 3x, 7x (The ratio is 1:3:7)

We know that Sum of all interior angles of a pentagon = 540

∴ x + 3x + 7x + 40 + 60 = 540

11x + 100 = 540

11x = 440

x = 40

∴ Desired angles are

x = 40

3x = 3×40 = 120

7x = 7×40 = 280

Hence Largest Angle is 280°