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Unit 7

Adjacent Angles

Angles, Triangles, and Prisms

Lesson 2

Expressions and Equations

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Let’s look at some special pairs of angles.

Unit 7 ● Lesson 2

Learning

Goal

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Estimating Angle Measures

Unit 7 ● Lesson 2 ● Activity 1

Estimate the degree measure of each indicated angle.

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Warm-up

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Cutting Rectangles

Unit 7 ● Lesson 2 ● Activity 2

Your teacher will give you two small, rectangular papers.

  • On one of the papers, draw a small half-circle in the middle of one side.

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  • Cut a straight line, starting from the center of the half-circle, all the way across the paper to make 2 separate pieces. (Your cut does not need to be perpendicular to the side of the paper.)
  • On each of these two pieces, measure the angle that is marked by part of a circle. Label the angle measure on the piece.
  • What do you notice about these angle measures?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Cutting Rectangles

Unit 7 ● Lesson 2 ● Activity 2

  • Clare measured 70 degrees on one of her pieces. Predict the angle measure of her other piece.
  • On the other rectangular paper, draw a small quarter-circle in one of the corners.

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  • Repeat the previous steps to cut, measure, and label the two angles marked by part of a circle.
  • What do you notice about these angle measures?
  • Priya measured 53 degrees on one of her pieces. Predict the angle measure of her other piece.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Cutting Rectangles

Unit 7 ● Lesson 2 ● Activity 2

  • Think back to the first piece of paper you cut.
    • What do you notice about the pairs of angle measures?
    • Why do you think this is?
    • Why do you think some people got measurements that do not sum to exactly 180 degrees?
  • Think about how you solved for the measure of Priya’s second angle compared to how you solved for the measure of Clare’s second angle. What was the same, and what was different?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Is It a Complement or Supplement?

Unit 7 ● Lesson 2 ● Activity 3

  • Use the protractor in the picture to find the measure of angles BCA and BCD.

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  • Explain how to find the measure of angle ACD without repositioning the protractor.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Is It a Complement or Supplement?

Unit 7 ● Lesson 2 ● Activity 3

  • Use the protractor in the picture to find the measure of angles LOK and LOM.

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  • Explain how to find the measure of angle KOM without repositioning the protractor.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Is It a Complement or Supplement?

Unit 7 ● Lesson 2 ● Activity 3

  • Angle BAC is a right angle. Find the measure of angle CAD.

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  • Point O is on line RS. Find the measure of angle SOP.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Is It a Complement or Supplement?

Unit 7 ● Lesson 2 ● Activity 3

  • Which other problem in this activity was similar to the third question? How?
  • Which other problem in this activity was similar to the last question? How?
  • The term complementary describes a pair of angles whose measures sum to 90 degrees, and the term supplementary describes a pair of angles whose measures sum to 180 degrees.
    • Which angles in this activity were supplementary angles?
    • Which angles in this activity were complementary angles?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Adjacent Angles

Unit 7 ● Lesson 2

  • What does it mean for two angles to be supplementary?
  • What does it mean for two angles to be complementary?
  • If you know two angles are supplementary and you know the measure of one angle, how can you find the other?

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Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Unit 7 ● Lesson 2

  • I can find unknown angle measures by reasoning about complementary or supplementary angles.
  • I can recognize when adjacent angles are complementary or supplementary.

Learning

Targets

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Finding Measurements

Unit 7 ● Lesson 2 ● Activity 4

  • Point F is on line CD. Find the measure of angle CFE.

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  • Angle SPR and angle RPQ are complementary. Find the measure of angle RPQ.

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Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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adjacent angles

Unit 7 ● Lesson 2

Adjacent angles share a side and a vertex.

In this diagram, angle ABC is adjacent to angle DBC.

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Glossary

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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complementary

Unit 7 ● Lesson 2

Complementary angles have measures that add up to 90 degrees.

For example, a 15° angle and a 75° angle are complementary.

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Glossary

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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right angle

Unit 7 ● Lesson 2

A right angle is half of a straight angle.

It measures 90 degrees.

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Glossary

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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straight angle

Unit 7 ● Lesson 2

A straight angle is an angle that forms a straight line.

It measures 180 degrees.

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Glossary

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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supplementary

Unit 7 ● Lesson 2

Supplementary angles have measures that add up to 180 degrees.

For example, a 15° angle and a 165° angle are supplementary.

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Glossary

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), https://creativecommons.org/licenses/by-nc/4.0/.

All curriculum excerpts are under the following licenses:

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

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