Mathematics The angles of the pentagon are in ratio 4 : 8 : 6 : 4 : 5. Find the greatest angle of the pentagon.Class: 10

The angles of the pentagon are in ratio 4 : 8 : 6 : 4 : 5. Find the greatest angle of the pentagon.

Class: 10

A
180°
B
160°
C
70°
D
60°

Solution:

Let the angles of the pentagon are 4x, 8x, 6x, 4x and 5x.
⇒ 4x + 8x + 6x + 4x + 5x = 540°
⇒ 27x = 540°
⇒ x = 20°
         Then the angles of pentagon are:
          4 × 20° = 80°
          8 × 20° = 160°
          6 × 20° = 120°
          4 × 20° = 80°
          5 × 20° = 100°

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