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Lesson 9

1. Lesson 9

1.4. Explore 3

Module 2: Lesson 9

Module 2: Logic and Geometry

 

Try This 2
 

exterior angle: an angle at a vertex of a triangle, outside the triangle, formed by one side and the extension of an adjacent side

 

This illustration is the exterior and interior angles in a triangle.

Determine the measures of the unknown angles in . Note that ∠MTH is an exterior angle of . Justify your reasoning. hint

 

 

This is a diagram of a triangle with an exterior angle, angle H. Angle A is 138 degrees. Exterior angle MTH is 168 degrees.

 

 

Share 1
 

Use your angle measurements from Try This 2 to answer the following questions with another student.

  1. Compare your angle measurements from Try This 2 with your partner’s measurements.

    • Did you get the same answers for the unknown angle measurements?

    • How were your methods for determining the unknown angles similar? How were they different?

  2. non-adjacent interior angles: two angles of a triangle that do not have the same vertex as an exterior angle

     

    This illustration is of two non-adjacent interior angles in a triangle.

    With your partner, make a conjecture about the relationship between an exterior angle (∠MTH) and its two non-adjacent interior angles (∠AMT and ∠MAT) based on your results.

If you are not sure where to begin and would like to see an example of this type of question, take a look at “Example 1: Using angle sums to determine angle measures” on page 87 of your textbook.