Question

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

Answer 1

Step-by-step explanation:

All the interior angles of a pentagon sum up to 540°.

Since these angles are in the above ratio,

Angle 1 = 5x

Angle 2 = 4x

Angle 3 = 7x

Angle 4 = 5x

Angle 5 = 6x

Therefore,

5x+4x+7x+5x+6x=540°

27x=540°

x=540/27=20°

Angle 1 = 5x=5 x 20=100°

Angle 2 = 4x=4 X 20=80°

Angle 3 = 7x=7 x 20=140°

Angle 4 = 5x=100°

Angle 5 = 6x= 6 x 20=120°

Check:

A1+A2+A3+A4+A5=540°

Answer 2

⠀⠀⠀⠀⠀ ☛...Given...☚⠀⠀ ⠀

⠀The ratio of interior angles of a Pentagon = 5 : 4 : 7 : 5 : 6

⠀⠀⠀ ⠀ ☛...To find...☚⠀⠀

⠀The value of each angle...

⠀⠀⠀⠀⠀ ☛...SoLution...☚⠀⠀

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

we know...

• 3 × 180°

Sum of all angles of a Pentagon is 540°

So,...

• 5x + 4x + 7x + 5x + 6x = 540°

• 27x = 540°

• x = 540°/ 27

• x = 20°

Put value of x...

• 5x = 5 × 20
• ⠀⠀= 100°

• 4x = 4 × 20
• ⠀⠀= 80°

• 6x = 6 × 20
• ⠀⠀= 120°

• 5x = 5 × 20
• ⠀⠀ = 100°

• 7x = 7 × 20
• ⠀ ⠀= 140°

________verification_______

⠀ ⠀⠀⠀5x + 4x + 7x + 5x + 6x = 540°

⠀⠀⠀⠀ 100° + 80° + 120° + 140° + 100° = 540°

⠀ ⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀540° = 540°⠀⠀

⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀L.H.S. = R.H.S.

________Hence verified_______