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Let's assume our polygon is a n-gon with n sides. So, there are an equal number of interior and exterior angles.
We know that:
1 Exterior + 1 Interior = will give us 180º
\ \ ________________\___________
Side of a trapezium using symbols.
Thus, the total of the exterior angles and interior angles will be 180nº [a]
As we know, the formula for the sum of interior angles is 180(n-2)º [b]
Subtracting [a] from [b], we get
180n - 180(n-2)
This can be simplified to
180(n-n+2)
Again, we can simplify that to
180*2
which gives us
360º
Thus, we have proved that the exterior angles of any polygon always equal 360º, no matter the number of sides.
What else can I help you with?
What shape equals 360 degrees?
The exterior angles of polygons equal 360 degrees.
Interior and exterior angles of a 30 sided polygon?
The total of the interior angles equal 5040, and each angle measures 168 degrees The total of the exterior angles equal 360, and each angle measures 12 degrees
What polygon does the sum of the measures of interior angles equal the sum of the measures of the exterior angles?
A 4 sided quadrilateral has interior angles that add up to 360 degrees and its exterior angles add up to 360 degrees
What is the exterior angle of an octagon?
The exterior angle of a general octagon is any angle less than 180 degrees. The sum of the exterior angles of a polygon is 360 degrees. If the octagon is regular, then each of its 8 exterior angles is equal to 360/8 = 45 degrees.
What shape has a exterior angle of 45 degrees?
Any shape can have an exterior angle of 45 degrees. If you are talking about exterior angle sum, it is always 360 degrees for any polygon. If you are talking about a regular polygon (equal exterior angles), it would be 360/45=8 sides. Therefore, a regular octagon has exterior angles of 45 degrees.
Are all polygons equal to 360 degrees?
The exterior angles of any polygon add up to 360 degrees
3 facts about regular polygons?
All sides are equal in lengthsEach interior angles are equal in sizeAll exterior angles add up to 360 degrees
Does the sum of exterior angles of a pentagon equal 300?
No, the sum of the exterior angles of any polygon, including a pentagon, is always 360 degrees, regardless of the number of sides. This is true for all polygons, meaning that the sum of the exterior angles of a pentagon is 360 degrees, not 300.
What shape equals 360 degrees?
The exterior angles of polygons equal 360 degrees.
The sum of exterior angles is equal to?
The sum of the exterior angles of a polygon is equal to 360 degrees.
What angles do a scalene triangle have?
-- A scalene triangle has three interior angles and three exterior angles. -- The sum of the interior angles is 180 degrees, and no two of them are equal. -- The sum of the exterior angles is also 180 degrees, and no two of them are equal. -- The sum of each interior angle and its adjacent exterior angle is 180 degrees.
What is the measure of an exterior angle of a regular polygon with 8 sides?
All polygons exterior angles sum to 360. If it is regular it means all angles are equal So all 8 angles are the same number 8x = 360 x = 45 Each angle is 45 degrees
Do internal angles of regular and irregular polygons always equal 360 degrees?
No, the sum of internal angles of polygons is represented by the equation 180(n-2) where n is the number of sides. The sum of the external angles, however, does always equal to 360 degrees.
Interior and exterior angles of a 30 sided polygon?
The total of the interior angles equal 5040, and each angle measures 168 degrees The total of the exterior angles equal 360, and each angle measures 12 degrees
What are exterior angles?
Exterior angles are the angles formed when a side of a polygon is extended, and they are adjacent to the interior angle at that vertex. In a polygon with n sides, there are n exterior angles, one at each vertex. The sum of the exterior angles of any polygon is always 360 degrees.
Are Exterior and interior angles equal to 360?
No because an exterior angle and an interior angle of a polygon add up to 180 degrees but exterior angles around a polygon add up to 360 degrees
What degrees does the outside of a triangle equal to?
The exterior angles of a triangle add up to 360 degrees.
