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Use what you know about the sum of a triangle's angles to solve these problems.

See if you can use the triangle sum theorem to find the missing information about angles inside a triangle. If you forget the procedure for solving these types of problems, refer to the steps below.

Identify the missing angle.
Use the triangle sum theorem to set up an equation.
Solve for the missing angle.

Select the correct answer to each of these questions. Then read the feedback carefully, especially if you answer the question incorrectly.

If a triangle has two interior angles that measure 106° and 39°, what is the measure of the third angle? 

  1. 45°
  2. 35°
  3. 25°

If you use the triangle sum theorem to solve this equation: 106° + 39° + x° = 180°, the missing angle x is equal to 35°.

If you use the triangle sum theorem to solve this equation: 106° + 39° + x° = 180°, the missing angle x is equal to 35°.

If you use the triangle sum theorem to solve this equation: 106° + 39° + x° = 180°, the missing angle x is equal to 35°.

What is the measure of the missing angle in this triangle?

question 2 triangle

  1. 160°
  2. 150°
  3. 129°

If you use the triangle sum theorem to solve this equation: 25° + 26° + x° = 180°, the missing angle x is equal to 129°. 

If you use the triangle sum theorem to solve this equation: 25° + 26° + x° = 180°, the missing angle x is equal to 129°. 

If you use the triangle sum theorem to solve this equation: 25° + 26° + x° = 180°, the missing angle x is equal to 129°. 

If two angles inside a triangle measure 47° and 43°, what is the measure of the third interior angle? 

  1. 90°
  2. 100°
  3. 110°

By the triangle sum theorem, 47° + 43° + x° = 180°. Therefore, the missing angle x measures 90°.

By the triangle sum theorem, 47° + 43° + x° = 180°. Therefore, the missing angle x measures 90°.

By the triangle sum theorem, 47° + 43° + x° = 180°. Therefore, the missing angle x measures 90°.

Find the missing value x in the following triangle.

question 4 triangle

  1. 4
  2. 5
  3. 6

According to the triangle sum theorem, 70° + 60° +(8x + 2)° = 180°. You can use the following steps to solve this equation:
130 + 8x + 2 = 180
132 + 8x = 180
8x = 48
x = 6 

According to the triangle sum theorem, 70° + 60° +(8x + 2)° = 180°. You can use the following steps to solve this equation:
130 + 8x + 2 = 180
132 + 8x = 180
8x = 48
x = 6 

According to the triangle sum theorem, 70° + 60° +(8x + 2)° = 180°. You can use the following steps to solve this equation:
130 + 8x + 2 = 180
132 + 8x = 180
8x = 48
x = 6 

Summary

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