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.

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.