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Angle Relationships: Complementary, Supplementary & Vertical

Seventh graders learn how angles relate — complementary angles add to 90°, supplementary to 180°, and vertical angles are equal — and use these rules to find missing angle measures.

Grade 7Geometry50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
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Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Identify complementary angles.
  • ✓Identify supplementary angles.
  • ✓Identify vertical angles.
  • ✓Find a missing angle.
Essential Question

When two lines cross, or two angles sit side by side, their measures are connected by hidden rules. What are those relationships, and how do they help you find a missing angle?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Angle Explorer · Interactive

The Angle Explorer

Project this and tap each angle relationship. Have students learn to spot complementary, supplementary, and vertical angles!

📐 Explore angle relationships — tap eachTry it

The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Hidden Connections

5 min

When two lines cross, the angles are connected — how?

👩‍🏫 Teacher Moves

  • Show crossing lines.
  • Ask how the angles relate.
  • Set the goal: angle relationships.

🎒 Student Actions

  • See the angles.
  • Wonder the link.
  • Predict the idea.
2

I Do — The Relationships

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Complementary = 90°.
  • Supplementary = 180°.
  • Vertical angles are equal.

🎒 Student Actions

  • Learn complementary.
  • Learn supplementary.
  • Learn vertical.
3

We Do — Explore Together

13 min

Class uses the Angle Explorer.

👩‍🏫 Teacher Moves

  • Tap each relationship.
  • Identify it in a figure.
  • Find a missing angle.

🎒 Student Actions

  • Tap each.
  • Identify it.
  • Find missing.
4

You Do — On Your Own

12 min

Students find angles.

👩‍🏫 Teacher Moves

  • Identify angle pairs.
  • Find missing angles.
  • Explain the relationship.

🎒 Student Actions

  • Identify pairs.
  • Find missing.
  • Explain it.
5

Close — Close

5 min

One figure.

👩‍🏫 Teacher Moves

  • Show an angle figure.
  • Find the missing angle.
  • Hand out the exit ticket.

🎒 Student Actions

  • Find it.
  • Explain it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics.

CCSS
7.G.5

Use facts about angle relationships to write and solve equations for unknown angles.

CCSS
7.G.5

Identify complementary, supplementary, vertical, and adjacent angles.

CCSS
7.G.2

Draw geometric figures with given conditions.

SMP
MP.7

Use angle structure to find unknowns.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Angle-pair picture cards.
  • Sentence frame: “___ angles add to ___.”
  • Use a protractor.

Support & Access

IEP / 504
  • Start with supplementary (straight line).
  • Use labeled diagrams.
  • Subtract to find the missing angle.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Write equations for unknown angles.
  • Solve with algebra (x + 30 = 90).
  • Use multiple relationships together.
Materials

What to gather

  • 📽️Projector / board
  • 📐Protractors
  • 💻The Angle Explorer
  • 📄Angle diagrams
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

complementarytwo angles that add to 90°supplementarytwo angles that add to 180°vertical anglesopposite, equal angles at a crossingadjacent anglesangles next to each otherright anglea 90° anglestraight anglea 180° anglevertexthe corner point of an angledegreea unit of angle measure
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
Two complementary angles — one is 30°. What is the other?
60° (they add to 90°).
QUESTION 2
Two supplementary angles — one is 110°. What is the other?
70° (they add to 180°).
QUESTION 3
When two lines cross, what is true about vertical (opposite) angles?
They are equal.

Going deeper? Angle equations.

Have students write and solve equations for missing angles, like “x + 40° = 90°.” A printable angle-relationships sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Angle RelationshipsFlip
Card 1
Term
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Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Angle RelationshipsQuiz
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Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Angle RelationshipsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: adjacent angles, complementary, degree, right angle, straight angle, supplementary, vertex, vertical angles
  1. the corner point of an angle
  2. a unit of angle measure
  3. a 180° angle
  4. angles next to each other
  5. two angles that add to 90°
  6. a 90° angle
  7. opposite, equal angles at a crossing
  8. two angles that add to 180°

Part B · Show what you learned

  1. Two complementary angles — one is 30°. What is the other?
  2. Two supplementary angles — one is 110°. What is the other?
  3. When two lines cross, what is true about vertical (opposite) angles?
Answer key — Part A: 1) vertex · 2) degree · 3) straight angle · 4) adjacent angles · 5) complementary · 6) right angle · 7) vertical angles · 8) supplementary
Part B: 1) 60° (they add to 90°). 2) 70° (they add to 180°). 3) They are equal.