The interior angles of a pentagon are in the ratio 5: 4: 7: 5: 6. Find each angle of a pentagon.
Answers
Answered by
2
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°
Answered by
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_______
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