The Exterior angle of regular polygon formula explained with examples

Learn and know what is the formula for exterior angle of regular polygon. Generally, regarding this we will study in geometry chapter especially in polygons concept.

The Exterior angle of regular polygon formula explained with examples

With respect to polygon, we have four important formulas. Among them exterior angle of a regular polygon formula is one. The other formulas are interior angle of regular polygon, sum of interior angles, and sum of exterior angles. Now we will learn what is an exterior angle? And also the formula for the exterior angle of a regular polygon.

What is mean by the word regular polygon in math?

We know what is mean by a polygon? Now regular polygon means the polygons equal sides (lengths) and angles are called as regular polygon.

The best and known example is “square”.

The meaning of the exterior angle of a regular polygon in math is?

Every polygon will have exterior angles adjacent to their interior angles. Generally, If we extend the any one line segment associated to interior angle we will get the exterior angle. Number of interior angles and number of exterior angles will be equal and this is equal to number of sides of a polygon.

Formula for exterior angle of regular polygon as follows:

For any given regular polygon, to find the each exterior angle we have a formula. By using this formula, easily we can find the exterior angle of regular polygon.

Exterior angle of regular polygon is given by \frac { { 360 }^{ 0 } }{ n } , where “n” is number of sides of a regular polygon.

Examples:

Now let us take some polygons and we will try to find out the each exterior angle of it.

The exterior angle of the regular pentagon is given as the \frac { { 360 }^{ 0 } }{ 5 }   = { 72 }^{ 0 } .

The exterior angle of the regular octagon is given as the \frac { { 360 }^{ 0 } }{ 8 }   = { 45 }^{ 0 } .

The exterior angle of the regular polygon with 16 sides is given as the \frac { { 360 }^{ 0 } }{ 16 }   = { 22.5 }^{ 0 } .

The exterior angle of the regular polygon with 24 sides is given as the \frac { { 360 }^{ 0 } }{ 24 }   = { 15 }^{ 0 } .

FAQ’s on Exterior angle of regular polygon:

If we know exterior angle then can we say what type of polygon is it?

Yes, we can say what type of polygon. If you find the ratio of { 360 }^{ 0 } and exterior angle, then you will get number of sides. So from this number of sides, easily we can say the type of the polygon.

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