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Q: What is the name of the regular polygon whose interior angles are twice its exterior angles?

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A Regular Polygon

octagon interior=135 exterior=45

A quadrilateral.

Hint: in a regular polygon interior plus exterior = 180o, always.

It is a regular 8 sided octagon whose interior angles are 135 degrees and its exterior angles are 45 degrees

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A Regular Polygon

octagon interior=135 exterior=45

An equilateral triangle.

A quadrilateral.

Square or rectangle

Hint: in a regular polygon interior plus exterior = 180o, always.

4 such as a square

Exterior angles are supplementary with interior angles, so 180-30=150

If exterior angles are 120 then interior angles must be 60 so you have an equilateral triangle

Interior angles 178 so exterior angles 2. Number of sides of any regular polygon = 360/exterior angle You polygon has 180 sides. Bet you're glad you didn't have to sketch it!

The easiest way to solve this is to use the exterior angles of the polygon. The sum of an exterior angle and interior angle is 180o. Also the sum of all the exterior angles of a polygon is 360o. As the polygon is regular, all the interior angles are the same and all the exterior angles are the same. So, for an interior angle of 172o the exterior angle is 180-172 = 8o. The sum of all the exterior angles is 360o so how many 8o make up 360o? 360/8=45. Thus the polygon with interior angles of 172o has 45 sides.

If the polygon has n sides, each exterior angle is 360/n degrees.The interior angle is 180 less exterior angle.

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