Angles in a Triangle

​The sum of the measure of the interior angles of a triangle equals 180°

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​This thereom has many proofs but the most elegant is often visual.

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​Notice what is happening in the video?

​​Three angles of a triangle were cut out so they could be joined together to make one big angle.

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​When joined together, their exposed sides form a straight line.

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​Therefore the sum of the three angles was a straight angle (180 degrees) !

Using the fact that both the interior angle sum of a triangle and the angle sum of a linear pair is 180 degrees, we get :

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180 = 36 + 32 + 111

​180 = 36 + 144

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​32 + 111 = 144

​Exterior angles are formed by extending one side of the triangle.

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​The exterior angle and its adjacent angle then form a linear pair.

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​The angles that are not part of the linear pair are often called "remote interior angles".

• ​​​ I can justify the Triangle Sum Theorem.

• ​I can use the Triangle Sum Theorem to solve problems about triangles.

• ​I can justify the Exterior Angle Theorem.

• ​I can use the Exterior Angle Theorem to solve problems about triangles.