The following diagrams give the theorems involving the exterior angles of triangles. Scroll down the page for more examples and solutions.
Exterior Angles of a Triangle
An exterior angle of a triangle is formed by any side of a triangle and the extension of its adjacent side.
The Exterior Angle Theorem states that
An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Find the values of x and y in the following triangle.
x + 50° = 92° (sum of opposite interior angles = exterior angle)
x = 92° – 50° = 42°
y + 92° = 180° (interior angle + adjacent exterior angle = 180°.)
y = 180° – 92° = 88°
What is an exterior angle and how to find the unknown exterior angle of a triangle?
The angles on a straight line add up to 180°.
The interior angles of a triangle add up to 180°
An exterior angle of a triangle is formed when any side is extended outwards.
How to find a missing angle outside of a triangle?
How to define the interior and exterior angles of a triangle and then state several theorems involving the interior and exterior angles of a triangle
The exterior angles of a triangle are the angles that form a linear pair with the interior angles by extending the sides of a triangle.
The sum of the exterior angles of a triangle and any polygon is 360 degrees.
The remote angles are the two angles in a triangle that are not adjacent angles to a specific exterior angle.
The sum of the remote interior angles is equal to the non-adjacent exterior angle.
Sum of Exterior Angles of a Triangle
Two column proof of the sum of the exterior angles of a triangle is 360 degrees.
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