Using Equations to Solve for Unknown Angles

5 min

Narrative

In this activity, students consider whether there is enough information given to solve for the unknown angle measures. In previous lessons, students were given the measures of some angles in a figure and asked to solve for another. In this warm-up, the figure contains two unknowns and students are asked to critique Tyler’s thinking (MP3).

The discussion addresses the case in which angles aa and bb are equal to each other, in preparation for future activities in this lesson that have multiple unknown angles with the same measure. 

Launch

Arrange students in groups of 2. Give students 1 minute of quiet think time, followed by time to discuss their reasoning with their partner. Follow with a whole-class discussion.

Student Task

Tyler thinks that this figure has enough information to figure out the values of aa and bb.

Do you agree? Explain your reasoning.

Two rays on the same side of line l meet at the same point to form 3 angles, a, 90 degrees, b.

Sample Response

I disagree with Tyler. Sample reasoning: We don’t know how much bigger aa is than bb. All we know for sure is that a+b=90a+b=90.

Synthesis

Invite students to share their reasoning until they reach an agreement that Tyler is incorrect.

Ask students to come up with an equation to represent the angle measures in the figure. (a+90+b=180a+90+b=180, or equivalent) Record their answers for all to see.

Display this image. Invite students to share how this figure is the same as the figure from the task and how it is different.

<p>Straight angle, split into 3 angles.</p>

If students do not mention any of these points, make sure to point them out:

  • Some things that are the same are the facts that there are still two angles with unknown measures and the measures of the three angles add up to 180 degrees. The two unknown angles are still complementary.
  • The main difference is that the two unknown angles have the same measure.
  • This figure can be represented with the equation a+90+a=180a +90 + a = 180, or equivalent.
  • Because both unknown angles have the same measure, we have enough information to know the value of aa.
  • a=45a=45
Standards
Building On
  • 7.EE.4·Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
  • 7.EE.B.4·Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
Addressing
  • 7.G.5·Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
  • 7.G.B.5·Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

15 min

10 min