find the interior angle of the heptagon whose interior angle are in the ratio 5 ratio 7 ratio 4 ratio 3 ratio 6 ratio 8 ratio 3
Answers
Answer :
The angles are 125° , 175° , 100° , 75° , 150° , 200° , 75°
Step-by-step explanation:
Given,
The interior angles of the heptagon are in the ratio 5 : 7 : 4 : 3 : 6 : 8 : 3
To find,
the interior angles = ?
Solution,
Let the interior angles of the heptagon be
- 5x
- 7x
- 4x
- 3x
- 6x
- 8x
- 3x
Sum of all interior angles of a polygon, having n sides = 180° (n−2)
Heptagon has 7 sides,
put n = 7
Sum of all interior angles of heptagon = 180° (7 - 2)
= 180° (5)
= 900°
Sum of all interior angles of heptagon = 900°
5x + 7x + 4x + 3x + 6x + 8x + 3x = 900°
36x = 900°
x = 900°/36
x = 25°
5x = 5(25°) = 125°
7x = 7(25°) = 175°
4x = 4(25°) = 100°
3x = 3(25°) = 75°
6x = 6(25°) = 150°
8x = 8(25°) = 200°
3x = 3(25°) = 75°
∴ The angles are 125° , 175° , 100° , 75° , 150° , 200° , 75°