This document provides a lesson on solving one-step equations applied to real-world geometry problems involving angles. It begins with examples of defining different types of angles and then works through examples of writing and solving equations to determine missing angle measures when given the measures of other angles. Students are asked to write and solve equations for multi-step word problems involving angles in situations like designing a parking lot or analyzing the reflection of light off a mirror. The lesson concludes with an exit ticket for students to explain their process for determining the appropriate equation to solve for a missing angle or variable.

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MODULE 4 Expressions and Equaons
Topic H: Applicaons of Equaons
Lesson 30: One‐Step Problems in the Real World
Student Outcomes
§ Students calculate missing angle measures by wring and solving equaons.

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Classwork
Opening Exercise
Draw an example of each term and write a brief description.
Acute
Obtuse
Less than 90°
Between 90° & 180°

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Right
Straight
Reflex
Exactly 90°
Exactly 180°
Between 180° & 360°

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∠ABC measures 90°. The angle has been separated into two angles. If one
angle measures 57°, what is the measure of the other angle?
How are these two angles related?
What equaon could we use to solve for x.
Now let’s solve.

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Example 2
Michelle is designing a parking lot. She has determined that one of the angels should
be 115°. What is the measure of angle x and angle y?
How is angle x related to the 115° angle?
What equaon would we use to show this?
How would you solve this equaon?
How is angle y related the angle that measures 115° ?

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Example 3
A beam of light is reflected off of a mirror. Below is a diagram of the reflected beam.
Determine the missing angle measure.
How are the angles in this queson related?
What equaon could we write to represent the situaon?
How would you solve an equaon like this?

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Exercises
Write and solve an equaon in each of the problems.
1. ∠ABC measures 90°. It has been split into two angles,
∠ABD and ∠DBC. The measure of the two angles is in a
rao of 2:1. What are the measures of each angle?

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2. Solve for x.

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3. Candice is building a rectangular piece of fence according to the plans her boss
gave her. One of the angles is not labeled. Write an equaon and use it to
determine the measure of the unknown angle.

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4. Rashid hit a hockey puck against the
wall at a 38° angle. The puck hit the wall
and traveled in a new direcon.
Determine the missing angle in the
diagram.

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5. Jaxon is creang a mosaic design on a rectangular table. He has added two pieces
to one of the corners. The first piece has an angle measuring 38° that is placed in the
corner. A second piece has an angle measuring 27° that is also placed in the corner.
Draw a diagram to model the situaon. Then, write an equaon and use it to
determine the measure of the unknown angle in a third piece that could be added to
the corner of the table.

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Closing
Please take out your exit ticket for Lesson 30, close your
binder, and complete the exit ticket. This will be collected.
§ Explain how you determined the equaon you used to solve for the missing angle or variable.
SPRINTS!!!

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Sprints Round 1 ~Page 1

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Sprints Round 1 ~Page 2

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Sprints Round 2 ~Page 1

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Sprints Round 2 ~Page 2