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Exterior Angles Of A Triangle




 
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More Lessons for Grade 6

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In this lesson, we will learn
  • about exterior angles of triangles
  • how to find the unknown exterior angle of a triangle
  • how to prove that the sum of exterior angles of a triangle is 360°


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.



Example :

Find the values of x and y in the following triangle.

Solution:

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°

The following video gives a definition of exterior angles and shows how to find the unknown exterior angle of a triangle




The following video shows an example of how to find the exterior angle of a triangle.
This video will define the interior and exterior angles of a triangle and then state several theorems involving the interior and exterior angles of a triangle.


 

Sum of Exterior Angles of a Triangle

This video provides a two column proof of the sum of the exterior angles of a triangle is 360 degree.



Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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