The exterior angle of a triangle is an angle formed by one side of the triangle and the extension of an adjacent side. Every triangle has six exterior angles, two at each vertex. An exterior angle of a triangle is equal to the sum of the opposite interior angles. The exterior angle inequality theorem states that the measure of any exterior angle of a triangle is greater than either of the opposite interior angles. This condition is satisfied by all six external angles of a triangle.
An exterior angle of a polygon is an angle that is supplementary to one of the interior angles of the polygon, has its vertex at the vertex of that interior angle, and is formed by extending one of the interior angles. The exterior angle must be larger than either one of them. The measure of the exterior angle at a vertex is unaffected by which side is extended: the two exterior angles that can be formed at a vertex by extending one of the interior angles are not equal.
The exterior angle formed at the vertices of a triangle are not equal. The exterior angle is equal to the sum of the two remote interior angles of the triangle. Since both of the exterior angles at a given vertex are supplementary to the same interior angle, the two exterior angles always have equal measures. Additionally, since vertical angles are congruent, the two exterior angles possible around a single vertex are congruent.
In conclusion, the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle.
📹 How To Calculate The Interior Angles and Exterior Angles of a Regular Polygon
This geometry video tutorial explains how to calculate the interior angles and the exterior angles of a regular polygon. Examples …
📹 Why do exterior angles of any polygon add up to 360°?
The exterior angles of any polygon, regardless of its number of sides, always add up to 360º. Why’s that so? In this video, we’ll …
Add comment