# Lesson 4Solving for Unknown Angles

Let’s figure out some missing angles.

### Learning Targets:

- I can reason through multiple steps to find unknown angle measures.
- I can recognize when an equation represents a relationship between angle measures.

## 4.1 True or False: Length Relationships

Here are some line segments.

Decide if each of these equations is true or false. Be prepared to explain your reasoning.

## 4.2 Info Gap: Angle Finding

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

If your teacher gives you the *problem card*:

- Silently read your card and think about what information you need to answer the question.
- Ask your partner for the specific information that you need.
- Explain to your partner how you are using the information to solve the problem.
- Solve the problem and explain your reasoning to your partner.

If your teacher gives you the *data card*:

- Silently read the information on your card.
- Ask your partner “What specific information do you need?” and wait for your partner to
*ask*for information.*Only*give information that is on your card. (Do not figure out anything for your partner!) - Before telling your partner the information, ask “Why do you need that information?”
- After your partner solves the problem, ask them to explain their reasoning and listen to their explanation.

## 4.3 What’s the Match?

Match each figure to an equation that represents what is seen in the figure. For each match, explain how you know they are a match.

### Are you ready for more?

- What is the angle between the hour and minute hands of a clock at 3:00?
- You might think that the angle between the hour and minute hands at 2:20 is 60 degrees, but it is not! The hour hand has moved beyond the 2. Calculate the angle between the clock hands at 2:20.
- Find a time where the hour and minute hand are 40 degrees apart. (Assume that the time has a whole number of minutes.) Is there just one answer?

## Lesson 4 Summary

We can write equations that represent relationships between angles.

- The first pair of angles are supplementary, so .
- The second pair of angles are vertical angles, so .
- The third pair of angles are complementary, so .

## Lesson 4 Practice Problems

is a point on line segment . is a line segment. Select

**all**the equations that represent the relationship between the measures of the angles in the figure.Which equation represents the relationship between the angles in the figure?

Segments , , and intersect at point , and angle is a right angle. Find the value of .

Select

**all**the expressions that are the result of decreasing by 80%.Andre is solving the equation . He says, “I can subtract from each side to get and then divide by 4 to get .” Kiran says, “I think you made a mistake.”

- How can Kiran know for sure that Andre’s solution is incorrect?
- Describe Andre’s error and explain how to correct his work.

Solve each equation.

A train travels at a constant speed for a long distance. Write the two constants of proportionality for the relationship between distance traveled and elapsed time. Explain what each of them means.

time elapsed (hr) distance (mi) 1.2 54 3 135 4 180