Before going to understand the amount of exterior angle formula, first, let us recall what is an exterior angle. One exterior edge of a polygon is the angle between a side and also its nearby extended side. This can be understood clearly by observing the exteriors angles in the listed below triangle. The amount of exterior angles formula states the amount of every exterior angle in any type of polygon is 360°.

You are watching: What is the measure of each exterior angle of a regular hexagon?

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What Is the amount of Exterior angle Formula?

From the above triangle, the exterior angles Y and also R comprise a direct pair.(Y + R = 180°). And this gives, Y = 180° - R.

Sum that all three exterior angles of the triangle:Y + R + Y + R + Y + R= 180° +180° +180°3Y + 3R = 540°

Sum of inner angles the a triangle:R + R + R =180°3R =180°.

Substituting this in the above equation:3Y + 180° = 540°3Y = 540° - 180°3Y = 360°

Therefore the amount of exterior angle = 360°

Thus, the sum of every exterior angle of a triangle is 360°. In the same way, we can prove that the sum of all exterior angle of any type of polygon is 360°. Thus, the amount of exterior angles can be derived from the following formula:

Sum that exterior angle of any kind of polygon = 360°

Each exterior angle of a constant polygon that n political parties = 360° / n.

Let us examine a few solved instances to learn much more about the sum of exterior angle formula.


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Solved instances on sum of Exterior angle Formula

Example 1:Find the measure of every exterior edge of a consistent hexagon.

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Solution:

To find: The measure up of every exterior edge of a continuous hexagon.

We understand that the number of sides the a hexagon is, n = 6.

By the amount of exterior angles formula,

Each exterior angle of a regular polygon the n sides = 360° / n.

Substitute n = 6 here:

Each exterior angle of a hexagon = 360° / 6 = 60°

Answer: each exterior edge of a consistent hexagon = 60°.

Example 2:Use the amount of exterior angle formula come prove the each internal angle and also its equivalent exterior angle in any kind of polygon aresupplementary.

Solution:

To prove: The amount of an interior angle and its equivalent exterior edge is 180°.

Let us consider a polygon that n sides.

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By the sum of exterior angles formula,

Sum that exterior angles of any polygon = 360°

By the amount of interior angles formula,

Sum of inner angles of any type of polygon = 180 (n - 2)°

By adding the above two equations, we acquire the amount of every n internal angles and the amount of every n exterior angles:

360° + 180 (n - 2)° = 360° + 180n - 360° = 180n

So the amount of one inner angle and its matching exterior edge is:

180n / n = 180°

Answer: An inner angle and also its equivalent exterior angle in any type of polygon space supplementary.