In these lessons, 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°

The following diagrams give the theorems involving the exterior angles of triangles. Scroll down the page for more examples and solutions.

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 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.

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.

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 calculator and problem solver 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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