Learn on PengiBig Ideas Math, Course 2Chapter 7: Constructions and Scale Drawings

Lesson 2: Complementary and Supplementary Angles

In this Grade 7 lesson from Big Ideas Math, Course 2, students learn to classify pairs of angles as complementary (summing to 90°) or supplementary (summing to 180°). Students also practice finding unknown angle measures by setting up and solving equations using these angle relationships. The lesson aligns with Florida standard MAFS.7.G.2.5 within the Chapter 7 unit on Constructions and Scale Drawings.

Section 1

Definitions of Complementary and Supplementary Angles

Property

If the sum of the measures of two angles is 180°, then the angles are supplementary.

If the sum of the measures of two angles is 90°, then the angles are complementary.

Examples

  • An angle measures 70°. Its supplement is 180° - 70° = 110° because supplementary angles must add up to 180°.
  • An angle measures 35°. Its complement is 90° - 35° = 55° because complementary angles must add up to 90°.

Section 2

Finding Unknown Angle Measures

Property

To find unknown angle measures in complementary and supplementary pairs:

  • For complementary angles: x+y=90°x + y = 90°
  • For supplementary angles: x+y=180°x + y = 180°

Set up an equation using the given information and solve for the unknown variable.

Book overview

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Chapter 7: Constructions and Scale Drawings

  1. Lesson 1

    Lesson 1: Adjacent and Vertical Angles

  2. Lesson 2Current

    Lesson 2: Complementary and Supplementary Angles

  3. Lesson 3

    Lesson 3: Triangles

  4. Lesson 4

    Lesson 4: Quadrilaterals

  5. Lesson 5

    Lesson 5: Scale Drawings

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Definitions of Complementary and Supplementary Angles

Property

If the sum of the measures of two angles is 180°, then the angles are supplementary.

If the sum of the measures of two angles is 90°, then the angles are complementary.

Examples

  • An angle measures 70°. Its supplement is 180° - 70° = 110° because supplementary angles must add up to 180°.
  • An angle measures 35°. Its complement is 90° - 35° = 55° because complementary angles must add up to 90°.

Section 2

Finding Unknown Angle Measures

Property

To find unknown angle measures in complementary and supplementary pairs:

  • For complementary angles: x+y=90°x + y = 90°
  • For supplementary angles: x+y=180°x + y = 180°

Set up an equation using the given information and solve for the unknown variable.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 7: Constructions and Scale Drawings

  1. Lesson 1

    Lesson 1: Adjacent and Vertical Angles

  2. Lesson 2Current

    Lesson 2: Complementary and Supplementary Angles

  3. Lesson 3

    Lesson 3: Triangles

  4. Lesson 4

    Lesson 4: Quadrilaterals

  5. Lesson 5

    Lesson 5: Scale Drawings