To aid you view what the sum of every exterior angle of a polygon is, we will use a square and also then a constant pentagon. Due to the fact that it is really easy to view what the amount is because that a square, us will begin with the square.

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Notice that an exterior angle is developed by a next of the square and also an extension of an nearby side. For example in the figure below, edge x, edge y, edge z, and angle w space all exterior angles.


Each interior angle in a square is same to 90 degrees. Notice that an interior angle add to the adjacent exterior edge is same to 180 degrees.

Interior angle  +  surrounding exterior edge = 180 degrees.


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In fact, the sum of ( the inner angle to add the exterior edge ) of any polygon always add up come 180 degrees. This is so because when girlfriend extend any type of side of a polygon, what you room really act is expanding a straight line and also a right line is always equal to 180 degrees.


For example, 90 levels + w = 180 degrees

90 degrees - 90 degrees + w = 180 levels - 90 degrees

0 + w = 90 degrees

w = 90 degrees

Since there are 4 exterior angles, 4 x 90 levels = 360 degrees.

Sum of all exterior angle of a polygon: pentagon


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In the number or pentagon above, we usage a to represent the internal angle the the pentagon and also we use x,y,z,v, and also w to represents the 5 exterior angles.

To uncover the measure of the interior angle of a pentagon, we just need to usage this formula.

<(n - 2 ) 180> / n 

Since n is same to 5, <(n - 2 ) 180> / n = <(5 - 2) 180> / 5 = <3 x 180> / 5 = 540 / 5 = 108

Again, interior angle  +  nearby exterior angle = 180 degrees.

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108 levels + surrounding exterior angle = 180 degrees

180 degrees - 180 levels + surrounding exterior angle = 180 degrees

0 + surrounding exterior angle = 180 degrees

Adjacent exterior angle = 180 degrees

Since there are 5 exterior angles, 5 x 72 = 360 degrees.

It walk not issue how many sides the polygon has, the sum of every exterior angle of a polygon is constantly equal to 360 degrees. 


Types that angles


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