This document provides examples and exercises for solving one-step problems involving angles. It begins with examples of defining different types of angles and two word problems involving angles that add up to 90 degrees. Students are asked to write equations to represent the relationships and solve for the missing angles. Several practice problems then ask students to write and solve equations to find missing angle measures in diagrams related to real-world contexts like designing a parking lot or mosaic.

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 30
Lesson 30: One-Step Problemsin the Real World
Classwork
OpeningExercise
Draw an example of each term and write a brief description.
Acute
Obtuse
Right
Straight
Reflex

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 30
Example 1
∠𝐴𝐵𝐶 measures 90°. The anglehas been separated into two angles. If one anglemeasures 57°, what is the measure of
the other angle?
How are these two angles related?
What equation could we use to solvefor 𝑥.
Now let’s solve.
Example 2
Michelleis designinga parkinglot. 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 equation would we use to showthis?
How would you solvethis equation?
How is angle 𝑦 related the anglethat measures 115° ?
115°𝑥°
𝑦°

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 30
Example 3
A beam of lightis reflected off of a mirror. Below is a diagramof the reflected beam. Determine the missingangle
measure.
How are the angles in this question related?
What equation could we write to represent the situation?
How would you solvean equation likethis?
Exercises
Write and solvean equation in each of the problems.
1. < 𝐴𝐵𝐶 measures 90°. It has been splitinto two angles, < 𝐴𝐵𝐷 and < 𝐷𝐵𝐶. The measure of the two angles is in a
ratio of 2: 1. What are the measures of each angle?
2. Solve for 𝑥.
64° 𝑥°
37°
𝑥°
55° 55°

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 30
𝑥°
49°
38°
𝑥°
38°
3. Candiceis buildinga rectangular pieceof fence accordingto the plans her boss gave her. One of the angles is not
labeled. Write an equation and use it to determine the measure of the unknown angle.
4. Rashid hita hockey puck againstthe wall ata 38° angle. The puck hit the wall and traveled in a new direction.
Determine the missinganglein the diagram.
5. Jaxon is creatinga mosaic design on a rectangular table. He has added two pieces to one of the corners. The first
piece has an anglemeasuring 38° that is placed in the corner. A second piece has an angle measuring 27° that is
also placed in the corner. Draw a diagramto model the situation. Then, write an equation and use itto 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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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 30
𝑥˚
52˚
Problem Set
1. Solve for 𝑥.
2. < 𝐵𝐴𝐸 measures 90°. Solve for 𝑥.
3. Thomas is puttingin a tilefloor. He needs to determine the angles that should be cut in the tiles to fitin the corner.
The angle in the corner measures 90°. One piece of the tilewill havea measure of 24°. Write an equation and use
it to determine the measure of the unknown angle.
4. Solve for 𝑥.
105°
62°
𝑥°

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 30
5. Aram has been studyingthe mathematics behind pinball machines. He made the followingdiagramof one of his
observations. Determine the measure of the missingangle.
6. The measures of two angles havea sum of 90°. The measures of the angles arein a ratio of 2:1. Determine the
measures of both angles.
7. The measures of two angles havea sum of 180°. The measures of the angles arein a ratio of 5: 1. Determine the
measures of both angles.
52°
68°
𝑥°