# 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.

Related Pages
Illustrative Math

#### 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. #### 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.

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