Lesson 15Adding the Angles in a Triangle
Let’s explore angles in triangles.
Learning Targets:
- If I know two of the angle measures in a triangle, I can find the third angle measure.
15.1 Can You Draw It?
- 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.
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Share your drawings with a partner. Discuss your thinking. If you disagree, work to reach an agreement.
acute (all angles acute) | right (has a right angle) | obtuse (has an obtuse angle) | |
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scalene (side lengths all different) | |||
isosceles (at least two side lengths are equal) | |||
equilateral (three side lengths equal) |
15.2 Find All Three
Your teacher will give you a card with a picture of a triangle.
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The measurement of one of the angles is labeled. Mentally estimate the measures of the other two angles.
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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.
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Enter the three angle measures for your triangle on the table your teacher has posted.
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?
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Draw a quadrilateral. Cut it out, tear off its angles, and line them up. What do you notice?
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Repeat this for several more quadrilaterals. Do you have a conjecture about the angles?
Lesson 15 Summary
A angle is called a straight angle because when it is made with two rays, they point in opposite directions and form a straight line.

If we experiment with angles in a triangle, we find that the sum of the measures of the three angles in each triangle is —the same as a straight angle!
Through experimentation we find:
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If we add the three angles of a triangle physically by cutting them off and lining up the vertices and sides, then the three angles form a straight angle.
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If we have a line and two rays that form three angles added to make a straight angle, then there is a triangle with these three angles.
Glossary Terms
A straight angle is an angle that forms a straight line. It measures 180 degrees.
Lesson 15 Practice Problems
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In triangle , the measure of angle is .
- Give possible measures for angles and if triangle is isosceles.
- Give possible measures for angles and if triangle is right.
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For each set of angles, decide if there is a triangle whose angles have these measures in degrees:
- 60, 60, 60
- 90, 90, 45
- 30, 40, 50
- 90, 45, 45
- 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.
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Angle in triangle is obtuse. Can angle or angle be obtuse? Explain your reasoning.
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For each pair of polygons, describe the transformation that could be applied to Polygon A to get Polygon B.
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On the grid, draw a scaled copy of quadrilateral using a scale factor of .