Angles in a Triangle

Angles in a Triangle

​ I can justify the Triangle Sum Theorem.

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​ I can justify the Exterior Angle Theorem.

​Triangle Sum Theorem

​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?

​So, ... What Happened?

​​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) !

Multiple Choice

Find the measure of the missing angle.

• 30^o
• 110^o
• 150^o
• 40^o

Multiple Choice

Can the following three angles form a triangle?

30°, 60°, 90°

• yes

• no

Multiple Choice

A student is trying to construct triangles using four different sets of angles. The angles in each set are given below. Which set will form a triangle?

• 45°, 65°, 70°

• 150°, 110°, 100°

• 50°, 50°, 50°

• 90°, 90°, 90°

​Exterior Angle Theorem

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

​Proving the using Triangle Sum Theorem...

​Exterior Angles on Polygons

​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".

Multiple Choice

Which two angles are the remote interior angles to Angle W?

• Angle X and Angle Y

• Angle X and Angle Z

• Angle Y and Angle Z

• Angle Z and Angle W

Multiple Choice

What is the measure of x?

• 101°

• 111°

• 121°

• 131°

Multiple Choice

Find the indicated angle measure. (What is ?)

• 51°

• 37°

• 167°

• 41°

​Summary

• ​​​ 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.