Respuesta :
Answer: 10 sides
=========================================================
Explanation:
x = exterior angle
x+108 = interior angle, as its 108 degrees larger than the exterior
The two angle pairs add up to 180, since they form a straight line
exterior+interior = 180
x+(x+108) = 180
2x+108 = 180
2x = 180-108
2x = 72
x = 72/2
x = 36
The exterior angle is 36 degrees which means we have n = 360/x = 360/36 = 10 sides. This polygon is a decagon.
Answer:
- 10 sides
Step-by-step explanation:
Let the number of sides is n.
We know the sum of interior angles is:
- 180(n - 2)
So each interior angle is:
- 180(n - 2)/n
We also know the sum of exterior angles is 360, so each exterior angle is:
- 360/n
We are given the difference of the interior and exterior angles:
- 180(n - 2)/n - 360/n = 108
Solve the equation for n:
- 180(n - 2) - 360 = 108n
- 180n - 360 - 360 - 108n = 0
- 72n = 720
- n = 10
The polygon has 10 sides