Question

The interior angles of a pentagon are in the ratio 4 : 5 : 6 : 7 : 5. Find each angle of the pentagon.

Answer 1

Answer:

Angles are 80°, 100°, 120°, 140°, 100°

Step-by-step explanation:

The interior angles of a pentagon are in the ratio 4:5:6:7:5.

Let angles are 4x,5x,6x,7x and 5x.

Sum of all angles of a polygon, having n sides = 180

o

(n−2)=180

o

(5−2)=540

o

Now,

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

o

27x=540

o

x=20

o

Angles are

4x=4×20

o

=80

o

5x=5×20

o

=100

o

6x=6×20

o

=120

o

7x=7×20

o

=140

o

5x=5×20

o

=100

o

Answer 2

Answer:

Let the angles be 4x,5x,6x,7x and 5x

Now, the sum of angles of a pentagon = 540°

So,

4x+5x+6x+7x+5x=540°

27x=540°

x=540/27

x=20°

Now, each angles are

• 4x= 4 x 20 = 80°
• 5x= 5 x 20 = 100°
• 6x= 6 x 20 = 120°
• 7x= 7 x 20 = 140°
• 5x= 5 x 20 = 100°