Question

The interior angle of a polygon is 108⁰ greater than the exterior angle. How many sides has the polygon​

Answer 1

Answer: 10 sides

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Step-by-step 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 2

• 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