Question

The angles of the pentagon are in the ratio 5:4:7:6:5. Find the value of the biggest and

the smallest angles.​

Answer 1

Question :-

The angles of the pentagon are in the ratio 5:4:7:6:5. Find the value of the biggest and  the smallest angle.

Aim :-

• To find the biggest and smallest angle of the figure

Given :-

• The figure is a pentagon
• The angles are in the ratio 5:4:7:6:5

In a pentagon the angles add up to 540°.

Since ratios are expressed in the simplest form,

Let the angles be :-

5x, 4x, 7x, 6x, 5x respectively.

By adding all these,

5x + 4x + 7x + 6x + 5x = 540

27x = 540

$x = \dfrac{540}{27}$

x = 20

Hence the angles are :-

5(20) , 4(20) , 7(20) , 6(20) , 5(20)

100°, 80°, 140°, 120°, 100°

Hope it helps!

Happy day!