Fishtank Learning

7th Grade Math
Unit 6: Geometry
Lesson 1

Objective

Identify and determine values of angles in complementary and supplementary relationships.

Warm Up

Look at the lines and angles of the roads in this diagram. What do you notice and wonder? What vocabulary can you use to describe the angles you see?

Fishtank Learning curriculum image

Anchor Problems - Problem 1

Use the diagram below to answer the questions.

Diagram showing line segments with angles and perpendicular lines at point B.

a. List as many different angles as you can.

b. Label the angles that you have listed as acute, obtuse, or right angles.

c. Name two sets of adjacent angles and two sets of nonadjacent angles.

Purpose

Optional This problem recalls and extends prior knowledge of angle types and angle notation. Students practice identifying acute, obtuse, and right angles, and naming adjacent and nonadjacent angles with precision. The work reinforces vocabulary from earlier grades while establishing the language and habits of precision to reason about angle relationships in subsequent problems MP.6 Attend to precision. . This Anchor Problem is optional depending on whether students would benefit from the review. It can also be included as part of an extended Warm Up or as part of the Problem Set, if desired.

Facilitation Guidance

Launch the problem by drawing students into the idea that angles are everywhere—in the corners of the room, the way desks meet, even the way their arms bend. Invite them to gesture or point out real-world examples as you review familiar vocabulary together: right angles, acute and obtuse angles, adjacent angles, straight angles. This frames the work not just as a diagram on paper, but as a way of noticing structure all around them. Use questions such as:
- What is an angle?
- What do you remember about different types of angles?
- Where do you see right angles, obtuse angles, and acute angles?
- Where do you see adjacent angles?
Have students work in pairs to examine the problem and determine how many different angles they can find. This primes vocabulary use, supports students in recalling how to name angles, and creates a baseline list that can be revisited as they notice additional angles that are made up of combined acute angles.
During work time, give students time to list angles and classify them. Notice how students make sense of $$\angle DBE$$, since it looks close to a right angle without the label. They may try to compare it to a corner of a piece of paper or other right angle, use tracing paper, or attempt to use a protractor MP.5 Use appropriate tools strategically. . Prompts to support and extend:
- What’s the problem with calling an angle by just its vertex?
- Why did you classify that as acute or obtuse?
- How can you be sure that $$\angle DBE$$ is not a right angle? What tools might you use?
- What makes these two angles adjacent or nonadjacent?
- Do you see any angles that could be measured two different ways?
- How many degrees are in a right angle? Straight line? Circle?
Debrief the problem by surfacing sticky points rather than just reviewing all parts of the problem. For example, you might:
- Discuss precision in naming and classifying, including angle names and mathematical terms, or clarify adjacent vs. nonadjacent angles.
- Address reflex angles if they arose. See Notes section for additional details.
- Highlight different strategies for systematically finding angles (scanning clockwise, starting with right angles, etc.) and validate multiple ways of seeing the structure MP.7 Look for and make use of structure. .
- Connect back to the warm-up context (real-world noticing) to reinforce that students are beginning to build a toolkit of vocabulary and precision that will be important when they solve for unknowns in later problems.

Anchor Problems - Problem 2

Your teacher will give you a set of cards. Your job is to sort the cards to create two groups: one that describes and gives examples of complementary angles and the other that describes and gives examples of supplementary angles. If a card shows a single angle measure, find a matching card that creates a complementary or supplementary pair before placing it in a group.

Definitions:

Complementary Angles: Two angles are complementary if their sum is 90°. Each angle is called the complement of the other.
Supplementary Angles: Two angles are supplementary if their sum is 180°. Each angle is called the supplement of the other.

Purpose

This Anchor Problem introduces the terms complementary angles and supplementary angles by connecting definitions, diagrams, and numerical examples. The sorting activity develops fluency with this vocabulary and with identifying pairs that sum to 90° or 180°.

Setup

Print enough copies of the Complementary and Supplementary Angles Sorting Cards on cardstock, so that each group gets one complete set. Have students cut the cards out in class, or prepare them ahead of time by cutting along the dotted lines.

Facilitation Guidance

Launch the problem by reading the definitions aloud and asking students to restate each one in their own words. Prompt:
- How would you explain complementary angles?
- How would you explain supplementary angles?
- How can you find pairs of angles that are supplements or complements?
Record and display student wording alongside the precise definitions to serve as a reference during the activity.
Have students work in pairs or groups of 3. Distribute the full card set to each group, and note the two kinds of cards (definitions/diagrams vs. angle measures). Invite them to share as a group what they notice and wonder and then to begin sorting. Encourage students to restate each other’s thinking as they work, using the key vocabulary.
- Provide sentence stems, such as “Angle ____ and ____ are complementary because…” or “Two supplementary angles are ____ and ____ because…”
- Prompt students to describe their choices explicitly.
Supporting Access for Students

If students would benefit from additional vocabulary support:
- Connect the terms complement and supplement to everyday language, such as:
  - “Complement” means to make something complete, so it sounds like “complete to 90°.”
  - “Supplement” means to add something extra, which makes it larger, so it can be remembered as “add up to 180°” (which is larger).
- Encourage students to share mnemonic devices or other cultural and linguistic connections that might help them remember.
- Demonstrate the meaning of complements and supplements multi-modally using manipulatives, drawings, and gestures.
Circulate to observe how students efficiently work to find pairs of angles that sum to 90° or 180°. Prompt groups to try out multiple approaches or ways of thinking about it. Look for some of the following to be able to discuss in the debrief:
- Some students may reason any angles greater than 90° must be part of a supplementary pair rather than complementary.
- Students may use the structure of the measures, seeing that 90° and 180° both have a zero in the ones place and reasoning that the pairs of measures will have digits that sum to ten in the ones place MP.7 Look for and make use of structure. .
- Some groups may use estimation to try to pair together angles before checking using addition or subtraction.
- If students attempt to use protractors to draw angles and place them together to see if they form right angles or straight lines, you may want to ask about the efficiency or precision of this strategy MP.5 Use appropriate tools strategically. .
Debrief the problem by engaging students in a discussion about efficient strategies to find complementary and supplementary pairs. Highlight student work that you observed while circulating, and prompt with questions such as:
- What is your strategy for finding pairs of angle measures that go together?
- How are right angles and straight lines related to these terms and these pairs of angles?
- Are complementary angles always adjacent angles? What about supplementary angles?
Supporting Access for Students

Increase engagement and participation in the discussion by asking students to consistently restate each other’s thinking. This could look like:
- After a student shares an approach, ask the class to restate what they heard to a partner using precise mathematical language.
- Select one or two students to share their restatement with the class, and ask the original speaker if their peer was able to accurately represent their thinking.
- Bring attention to words and phrases that clarify or draw out the meaning of the original explanation.

Notes

Students often associate supplementary angles only with straight lines and complementary angles only with right angles. If students seem to be assuming that the angles must be adjacent, point out that while this can be true, it doesn’t have to be—any two angles that sum to 90° or 180° meet the definitions. If helpful, show a diagram such as the one shown below to emphasize this idea:

Fishtank Learning curriculum image

Anchor Problems - Problem 3

In the diagram below, point $$P$$ lies on line $${QT}$$.

Triangle with angle labeled 38° and another angle labeled x°, forming a right angle at P.

a. Write and solve an equation to find the measure of $$x$$.

b. What is the measure of $$\angle RPT$$?

Purpose

This problem invites students to apply complementary and supplementary relationships to write and solve equations for unknown angle measures. It reinforces the precision of geometric vocabulary while showing that different equations can model the same situation MP.6 Attend to precision. MP.7 Look for and make use of structure. . Building on the sorting activity in Anchor Problem 2, this task deepens students’ understanding by connecting angle sums to algebra and composition of angles.

Facilitation Guidance

Launch the problem by displaying the diagram and inviting students to describe what they notice. Encourage them to use precise vocabulary: acute, right angle, straight angle, supplementary, complementary. Ask:
- What do you already know about the relationships among these angles?
- What labels can you add before you start solving?
This primes students to connect language and structure before jumping into equations. Frame the work of solving for unknowns like working through a puzzle to invite students to lean into the reasoning rather than only computation and spotlight the joy in geometry problems CRMT Culturally Responsive Math Teaching .
During work time, have students try the problem individually first, then compare equations with a partner. As you circulate, look for the different ways students might represent the relationship using supplementary and complementary relationships. Prompt them to use the mathematically precise terms as they explain their thinking to their partners. Ask questions such as:
- What pairs of angles do you see?
- How did you decide which angles to combine in your equation?
- What does each part of your equation represent in the diagram?
- Could there be another way to write the equation? Will it give the same solution?
- How do you know whether you are using a complementary or supplementary relationship?
Debrief the problem by comparing and connecting the different solution pathways and equations. Draw out the similarities by prompting students to ask each other questions and explain their reasoning.
- Some students may start with the straight line relationship of the three angles, and write an equation directly from that, such as 38 + $$x$$ + 90 = 180. Ask:
  - Can you write a parallel equation that uses the angle names? ($$\angle QPR$$ + $$\angle RPS$$ + $$\angle SPT$$ = 180)
  - Where did the different measures come from? For example, how did you know that $$\angle SPT$$ was 90°?
  - Do you see two angles that are supplementary in the structure of this diagram and in your equation?
  - How might you use parentheses to show the complementary and supplementary relationships?
- If students start with a simpler equation such as 38 + $$x$$ = 90, celebrate their fluency with quantitative reasoning and prompt them to deconstruct it for the class. Ask:
  - Can you write a parallel equation that uses the angle names? ($$\angle QPR$$ + $$\angle RPS$$ = 90)
  - Where did the different measures come from? For example, how did you know that these two angles sum to 90° if that is not labeled in the diagram directly?
  - How does this equation compare to other groups’ equations?

Notes

There is more than one equation that students may write to represent and find the measure of angle $$x$$. Highlight different equations that you see and discuss what angle relationships they involve. Solve each one to demonstrate they all result in the same value for $$x$$.
Supplements (or complements) are defined as pairs of angles. While three angles can together sum to 180°, they are not considered a “pair of supplementary angles.” In this problem, the supplementary pair consists of $$\angle QPS$$ and $$\angle SPT$$.

Problem Set

View Problem Set

Target Task

In the diagram below, point $$A$$ lies on line $${BD}$$ and $$\angle CAE$$ is a right angle.

Triangle with points A, B, C, D, and E, where A lies on BD and CAE is a right angle.

a. Describe the relationship between $$\angle DAE$$ and $$\angle EAB$$.

b. Name two angles that are complementary.

c. If the measure of angle $$DAC$$ is 74°, what is the measure of angle $$ DAE$$?

Fishtank Learning

7th Grade MathUnit 6: GeometryLesson 1

Objective

Warm Up

Anchor Problems - Problem 1

Anchor Problems - Problem 2

Anchor Problems - Problem 3

Problem Set

Target Task

7th Grade Math
Unit 6: Geometry
Lesson 1