How To Find Exterior Angle

Exterior angles of a polygon are formed when by one of its side and extending the other side. The sum of all the outside angles in a polygon is equal to 360 degrees. Y'all are already aware of the term polygon. A polygon is a flat figure that is made up of iii or more line segments and is enclosed. The line segments are chosen the sides and the point where two sides come across is chosen the vertex of the polygon. The pair of sides that meet at the aforementioned vertex are called adjacent sides. An angle at i of the vertices is called the interior angle. The internal and exterior angles at each vertex varies for all types of polygons. At present, permit us learn in detail the concept of its exterior angles.

What are Exterior Angles?

An exterior angle is an angle which is formed by one of the sides of whatsoever closed shape structure such as polygon and the extension of its next side. Encounter the figure below, where a five-sided polygon or pentagon is having 5 vertexes. The exterior angles of this pentagon are formed past extending its next sides.

Exterior angle

They are formed on the outside or exterior of the polygon.
The sum of an interior angle and its corresponding exterior angle is e'er 180 degrees since they lie on the same straight line.
In the figure, angles 1, ii, iii, 4 and five are the outside angles of the polygon.

Note: Exterior angles of a regular polygon are equal in measure.

Also, read:

Polygon
Polygon Curve Angle
Area Of Polygon
Perimeter Of Polygons

Sum of the Exterior Angles of a Polygon

Let united states say yous start travelling from the vertex at angle 1. You lot go in a clockwise direction, make turns through angles 2, three, 4 and 5 and come back to the same vertex. Yous covered the entire perimeter of the polygon and in fact, made one complete plough in the process. Ane consummate turn is equal to 360 degrees. Thus, information technology can be said that ∠1, ∠ii, ∠3, ∠4 and ∠5 sum upwardly to 360 degrees.

Hence, the sum of the measures of the outside angles of a polygon is equal to 360 degrees, irrespective of the number of sides in the polygons.

Polygon Outside Angle Sum Theorem

If a polygon is a convex polygon, then the sum of its outside angles (1 at each vertex) is equal to 360 degrees. Let us prove this theorem:

Proof: Consider a polygon with north number of sides or an n-gon. The sum of its exterior angles is N.

For any closed structure, formed by sides and vertex, the sum of the exterior angles is ever equal to the sum of linear pairs and sum of interior angles. Therefore,

Due north = 180n – 180(n-2)

N = 180n – 180n + 360

N = 360

Hence, nosotros got the sum of exterior angles of due north vertex equal to 360 degrees.

Video Lesson on Bending sum and exterior bending property

Exterior Angles Examples

Example 1: In the given figure, discover the value of x.

Exterior angle example

Solution: We know that the sum of exterior angles of a polygon is 360 degrees.

Thus, 70° + 60° + 65° + 40° + x = 360°

235° + x = 360°

10 = 360° – 235° = 125°

Example 2: Place the type of regular polygon whose exterior angle measures 120 degrees.

Solution: Since the polygon is regular, the measure out of all the interior angles is the same. Therefore, all its exterior angles measure the same besides, that is, 120 degrees.

Since the sum of exterior angles is 360 degrees and each ane measures 120 degrees, we accept,

Number of angles = 360/120 = 3

Since the polygon has three exterior angles, it has 3 sides. Hence it is an equilateral triangle.