Question

The difference between the interior and the exterior angle of a regular polygon is 90 degree. How
many sides does the polygon have?

Answer 1

Answer:

The sum of the exterior angles of all polygons is 360°. The sum of the interior angles of a polygon is (n - 2)180°. n is the number of sides. 90° is not possible.

Answer 2

Step-by-step explanation:

Let the interior angle and exterior angle of the regular polygon be x° and y° respectively.

We know that their sum is 180°.

• So x+y= 180°…..(1)

Also given that the difference between the interior angle and exterior angle = 90°

• Hence, x-y=90°………(2)

Subtracting (2) from (1)

we have,

• x+y - (x - y) = 180-90
• x + y - x + y = 90
• 2y=90
• $y = \frac{90}{2} = 45$

Hence each exterior angle = 30°.

Therefore the number of sides =

$\frac{360}{ext \: angle} = \frac{360}{45} = 8$

So the regular polygon has 8 sides.

hope it's helpful