maths

prove that the exterior angle of polygon is 360

1. 👍 0
2. 👎 0
3. 👁 107
1. From the centre of a polygon of n-sides (n-gon), draw rays towards the n-vertices thus forming n triangles.

The sum of internal angles of the n triangles equals 180n°. This sum also equals the sum of the n interior angles plus the angles around the central point, 360°. Call this sum A.

Extend each side of the n-gon to create an exterior angle. The sum of the exterior angle and the corresponding interior angle equals 180°. So the sum of all the exterior angles and interior angles of the n-gon equals 180n°. Call this sum B.

Since both equal 180n°,
sum A = sum B, or
360°+∑interior angles = ∑exterior angles + ∑ interior angles
Cancel out ∑interior angles, we get
∑exterior angles = 360°.

1. 👍 0
2. 👎 0

Similar Questions

1. maths

each interior angle of a regular polygon is 18 degree more than eight times an exterior angle. the number os sides of polygon is.

asked by polygon on March 28, 2012
2. Geometry

An exterior angle of an isosceles triangle has measure 150°. Find two possible sets of measures for the angles of the triangle. If the exterior angle of the bases is 150°​, then the measure of the angle of each base is _° and

asked by Hannah on December 18, 2016
3. geometry

if each angle in a regular polygon is 157.5 degrees, how many sides does the polygon have?

asked by Anonymous on September 23, 2009
4. geometry

The Polygon Angle-Sum Theorem states the following: The sum of the measures of the angles of an n-gon is ____. (1 point) (n – 1)180o (n – 2)180o 9. What is the measure of one angle in a regular 16-gon? (1 point) 2,520o 202.5o

asked by josh on December 31, 2012
1. math

The measure of an interior angle of a regular polygon is 135 degrees. Find the number of sides in the polygon. This is what I tried: 180(x-2)=135 [Interior Angle Sum Theorem] x-2=.75 x=2.75 That can't be right though. Help? Not

asked by Emily on March 27, 2007
2. Math

An irregular polygon has its exterior angles as 140,120,142,132,112 n x degrees Find the value of x.

asked by Phinehas on April 4, 2017
3. Math

Each exterior angle of a regular polygon is 15 degrees. How many sides does the polygon have? and What is the sum of the interior angles? Since this is not my area of expertise, I searched Google under the key words "polygon

asked by Shay on April 4, 2007
4. Algebra 2

The formula A = 180(n-2)/n relates to the measure A of an interior angle of a regular polygon to the number of sides n. If an interior angle measures 120 degrees, find the number of sides A)5 B)6 C)8 D)10 I have NO clue on how to

asked by erin on July 15, 2007
1. Geometry

Given: Segment CE bisects

asked by Kara on November 8, 2012
2. geometry

What is the relationship between the measure of a central angle of a polygon and the measures of an interior and an exterior angle of the polygon?

asked by sam on August 20, 2009
3. Geometry

m∠1 = 6x and m∠3 = 120. Find the value of x for p to be parallel to q. The diagram is not to scale. *114 *126 *120 *20 Find the values of x, y, and z. The diagram is not to scale. (38*, 56*,19*,x*,z*,y*) *x = 86, y = 94, z =

asked by Anonymous on November 12, 2010
4. Identifying patterns

If the pattern of polygons continues, how many sides will polygon 98 have? and there is a picture of polygon 1 which is a 3-sided triangle polygon 2- which is is a sqaure polygon 3- which is a 5 sided pentagon. polygon 4- which is

asked by Chelsea on May 11, 2011