Illustrative Mathematics Grade 8, Unit 1, Lesson 15: Adding the Angles in a Triangle

Learning Targets:

  • If I know two of the angle measures in a triangle, I can find the third angle measure.

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Illustrative Math
Grade 8

Lesson 15: Adding the Angles in a Triangle

Let’s explore angles in triangles.

Illustrative Math Unit 8.1, Lesson 14 (printable worksheets)

Lesson 15 Summary

The following diagrams show how the sum of angles in a triangle is 180 degrees.
Angles in Triangle

Lesson 15.1 Can You Draw It?

  1. Complete the table by drawing a triangle in each cell that has the properties listed for its column and row. If you think you cannot draw a triangle with those properties, write “impossible” in the cell.
  2. Share your drawings with a partner. Discuss your thinking. If you disagree, work to reach an agreement.

Lesson 15.2 Find All Three

Your teacher will give you a card with a picture of a triangle.

  1. The measurement of one of the angles is labeled. Mentally estimate the measures of the other two angles.
  2. Find two other students with triangles congruent to yours but with a different angle labeled. Confirm that the triangles are congruent, that each card has a different angle labeled, and that the angle measures make sense.
  3. Enter the three angle measures for your triangle on the table your teacher has posted.

Lesson 15.3 Tear It Up

Your teacher will give you a page with three sets of angles and a blank space. Cut out each set of three angles. Can you make a triangle from each set that has these same three angles?

Are you ready for more?

  1. Draw a quadrilateral. Cut it out, tear off its angles, and line them up. What do you notice?
  2. Repeat this for several more quadrilaterals. Do you have a conjecture about the angles?

Lesson 15 Practice Problems

  1. In triangle ABC, the measure of angle A is 40°.
    a. Give possible measures for angles B and C if triangle ABC is isosceles.
    b. Give possible measures for angles B and C if triangle ABC is right.
  2. For each set of angles, decide if there is a triangle whose angles have these measures in degrees:
    a. 60, 60, 60
    b. 90, 90, 45
    c. 30, 40, 50
    d. 90, 45, 45
    e. 120, 30, 30
    If you get stuck, consider making a line segment. Then use a protractor to measure angles with the first two angle measures.
  3. Angle A in triangle ABC is obtuse. Can angle B or angle C be obtuse? Explain your reasoning.
  4. For each pair of polygons, describe the transformation that could be applied to Polygon A to get Polygon B.
  5. On the grid, draw a scaled copy of quadrilateral ABCD using a scale factor of 1/2.

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

Try the free Mathway calculator and problem solver below to practice various 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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