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If the measure of the interior angle of a regular polygon is 90° greater than the measure of its exterior angle, then how many sides does it have?

If the measure of the interior angle of a regular polygon is 90° greater than the measure of its exterior angle, then how many sides does it have? Correct Answer 8

Given:

Interior angle = Exterior angle + 90° 

Concept used:

Interior angle + Exterior angle = 180° 

Formula used:

Number of sides of the polygon = (360°)/(Exterior angle)

Where, 

n = number of sides of the polygon 

E = Exterior angle

I = Interior angle

Calculation:

According to the question,

Interior angle = Exterior angle + 90° 

⇒ I = E + 90°      ----(1)

We know that,

⇒ I + E = 180° 

From equation (1)

⇒ E + 90° + E = 180° 

⇒ 2E = 90° 

⇒ E = 45°      ----(2)

Now,

Number of sides of the polygon = (360°)/(Exterior angle)

⇒ n = (360°/45°)

⇒ n = 8

∴ The regular polygon has 8 sides.

Additional Information

1) Regular Polygon: If all sides of any polygon are equal, the polygon is called a regular polygon.

 

 

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