What is the sum of exterior angles in a polygon?

Answer

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Hint: In this problem we need to know that the sum of all the interior angles in any of the polygon is 180(n-2) where n is the number of sides present in the polygon. We will consider any of the polygon here and then solve it to get the sum of exterior angles in the polygon. Doing this will solve your problem.

Complete step by step answer:

Polygon: A plane shape (two-dimensional) with straight sides. Examples: triangles, rectangles and pentagons. A circle is not a polygon because it is curved and has no side.

Here we need to find the sum of exterior angles of the polygon and in any of the polygons the sum of exterior angles is the same and the procedure of finding it is also the same. We need to remember this angle for various problems.

We will consider the pentagon here to find the sum of its exterior angle. The pentagon can be drawn as,

Here we can clearly see that a, b, c, d, e are the exterior angles of the polygon which is pentagon here and 1, 2, 3, 4 and 5 are the interior angles of the polygon.

We know that the sum of all the interior angles in ant of the polygon is

180(n-2) where n is the number of sides present in the polygon.

Here the value of n is 5 so the sum of all the interior angles is

1 + 2 + 3 + 4 + 5 = 180(5-2) = 180(3) = 540 degrees…………(1)

We know that linear angle is 180 degrees so, we can say that

Angle a + Angle 5 = 180

Therefore there are five exterior angles in the polygon here,

Therefore the angle a = 180 – angle 5 which is nothing but 180 – interior angle.

Similarly we can find all the exterior angles.

So, the sum of exterior angles is a + b + c + d + e = 5(180) – sum of interior angles.

So, we do from (1) a + b + c + d + e = 5(180) – 540 = 900 – 540 = 360 degrees.

Therefore sum of exterior angles in any of the polygon is 360 degrees.

Note: Whenever you get to solve such problems you need to draw the diagram and need to know that the sum of all the interior angles in ant of the polygon is 180(n-2) where n is the number of sides present in the polygon and then solve by this method. Remembering this that the sum of exterior angles in any of the polygons is 360 degrees will be very helpful in various problems. One can solve it by assuming n as the number of sides as well. Doing this will solve your problem.

Complete step by step answer:

Polygon: A plane shape (two-dimensional) with straight sides. Examples: triangles, rectangles and pentagons. A circle is not a polygon because it is curved and has no side.

Here we need to find the sum of exterior angles of the polygon and in any of the polygons the sum of exterior angles is the same and the procedure of finding it is also the same. We need to remember this angle for various problems.

We will consider the pentagon here to find the sum of its exterior angle. The pentagon can be drawn as,

Here we can clearly see that a, b, c, d, e are the exterior angles of the polygon which is pentagon here and 1, 2, 3, 4 and 5 are the interior angles of the polygon.

We know that the sum of all the interior angles in ant of the polygon is

180(n-2) where n is the number of sides present in the polygon.

Here the value of n is 5 so the sum of all the interior angles is

1 + 2 + 3 + 4 + 5 = 180(5-2) = 180(3) = 540 degrees…………(1)

We know that linear angle is 180 degrees so, we can say that

Angle a + Angle 5 = 180

Therefore there are five exterior angles in the polygon here,

Therefore the angle a = 180 – angle 5 which is nothing but 180 – interior angle.

Similarly we can find all the exterior angles.

So, the sum of exterior angles is a + b + c + d + e = 5(180) – sum of interior angles.

So, we do from (1) a + b + c + d + e = 5(180) – 540 = 900 – 540 = 360 degrees.

Therefore sum of exterior angles in any of the polygon is 360 degrees.

Note: Whenever you get to solve such problems you need to draw the diagram and need to know that the sum of all the interior angles in ant of the polygon is 180(n-2) where n is the number of sides present in the polygon and then solve by this method. Remembering this that the sum of exterior angles in any of the polygons is 360 degrees will be very helpful in various problems. One can solve it by assuming n as the number of sides as well. Doing this will solve your problem.

Last updated date: 29th Aug 2023

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