Question

Proof that the sum of measure of the external angle of any polygon is 360°

Answer 1

Answer:

We know that if we have to find the measure of an exterior angle of a polygon, we use the formula: 360/n, where n is the number of sides of the polygon.

One way to prove that the sum of exterior angles of a polygon is always 360°:

Let’s take for an example, a triangle as our polygon.

Let the ratio of the interior angles of our polygon be 1:2:3

1x+2x+3x= 180 (because the sum of interior angles is 180)

6x= 180

X= 30

The angles are:

30°, 60°, 90°

Now, we will find out the exterior angles of a triangle.

In the figure, we can see the lines FBC, BCD and AE are forming linear pairs. The angle sum of a linear pair is 180°.(The figure is in the attachment.)

∠ABF= 180-90

∠ABF= 90°

∠ACD= 180-60

∠ACD= 120°

∠CAE= 180-30

∠CAE= 150°

Sum of exterior angles= 150+120+90

= 150+210

= 360°

Using this process on any polygon, we can prove that the sum of exterior angles of a polygon is always 360°.

P.S.- The formula to find interior angles of a polygon:-

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

Hope my answer helps you.

Please mark my answer as BRAINLIEST.