Sum of Exterior Angles Formula

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What’s the exterior angle of an everyday hexagon

Sum of Exterior Angles Method

Earlier than going to know the sum of exterior angles method, first, allow us to recall what’s an exterior angle. An exterior angle of a polygon is the angle between a aspect and its adjoining prolonged aspect. This may be clearly understood by observing the exteriors angles within the beneath triangle. The sum of exterior angles method says the sum of all exterior angles in any polygon is 360°.

exterior and interior angles of a triangle

Studying: what’s the exterior angle of an everyday hexagon

What Is the Sum of Exterior Angles Method?

From the above triangle, the outside angles Y and R make up a linear pair.( Y + R = 180°). And this provides, Y = 180° – R.

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

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

Substituting this within the above equation: 3Y + 180° = 540° 3Y = 540° – 180° 3Y = 360°

Due to this fact the Sum of exterior angles = 360°

Thus, the sum of all exterior angles of a triangle is 360°. In the identical means, we will show that the sum of all exterior angles of any polygon is 360°. Thus, the sum of exterior angles may be obtained from the next method:

Sum of exterior angles of any polygon = 360°

Every exterior angle of an everyday polygon of n sides = 360° / n.

Allow us to verify a number of solved examples to study extra concerning the sum of exterior angles method.

Solved Examples on Sum of Exterior Angles Method

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Instance 1: Discover the measure of every exterior angle of an everyday hexagon.

exterior angle of a hexagon

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Resolution:

To search out: The measure of every exterior angle of an everyday hexagon.

We all know that the variety of sides of a hexagon is, n = 6.

By the sum of exterior angles method,

Every exterior angle of an everyday polygon of n sides = 360° / n.

Substitute n = 6 right here:

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

Reply: Every exterior angle of an everyday hexagon = 60°.

Instance 2: Use the sum of exterior angles method to show that every inside angle and its corresponding exterior angle in any polygon are supplementary.

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Resolution:

To show: The sum of an inside angle and its corresponding exterior angle is 180°.

Allow us to contemplate a polygon of n sides.

By the sum of exterior angles method,

Sum of exterior angles of any polygon = 360°

By the sum of inside angles method,

Sum of inside angles of any polygon = 180 (n – 2)°

By including the above two equations, we get the sum of all n inside angles and the sum of all n exterior angles:

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

So the sum of 1 inside angle and its corresponding exterior angle is:

180n / n = 180°

Reply: An inside angle and its corresponding exterior angle in any polygon are supplementary.

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