A given angle has measurement 227 degrees. A coterminal angle to this could have which of the following measurements? Be sure to check ALL correct answers! O A) 133° B) 947° C) –853° O D) –47° O E) 3827° O F) 587°
A given angle has measurement 227 degrees. A coterminal angle to this could have which of the following measurements? Be sure to check ALL correct answers! O A) 133° B) 947° C) –853° O D) –47° O E) 3827° O F) 587°
Elementary Geometry For College Students, 7e
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Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
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Chapter5: Similar Triangles
Section5.3: Proving Triangles Similar
Problem 1E: What is the acronym that is used to represent each statement? a Corresponding angles of similar...
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![**Question:**
A given angle has a measurement of 227 degrees. A coterminal angle to this could have which of the following measurements? Be sure to check all correct answers!
**Options:**
- A) 133°
- B) 947°
- C) -853°
- D) -47°
- E) 3827°
- F) 587°
**Explanation:**
To find coterminal angles, you can add or subtract full rotations (360 degrees) from the given angle. For a given angle θ, coterminal angles can be found using the formula:
θ + 360n
where n is any integer (positive, negative, or zero).
Let's determine if each of these options is coterminal with 227 degrees.
- **A) 133°**
\[
227° - 360° = -133°
\]
Since -133° is different from 133°, this is not a correct answer.
- **B) 947°**
\[
947° - 360° \times 2 = 227°
\]
Since 947° is coterminal with 227°, this is a correct answer.
- **C) -853°**
\[
-853° + 360° \times 3 = 227°
\]
Since -853° is coterminal with 227°, this is a correct answer.
- **D) -47°**
\[
-47° + 360° \times 1 = 313°
\]
Since 313° is different from 227°, this is not a correct answer.
- **E) 3827°**
\[
3827° - 360° \times 10 = 227°
\]
Since 3827° is coterminal with 227°, this is a correct answer.
- **F) 587°**
\[
587° - 360° = 227°
\]
Since 587° is coterminal with 227°, this is a correct answer.
Therefore, the correct answers are B) 947°, C) -853°, E) 3827°, and F) 587°.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd24861ef-92b0-4cd8-8c54-2ac2200498ec%2Fe92a4e16-73fa-4bec-94b6-cfbabec01d6b%2Fxntdk5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
A given angle has a measurement of 227 degrees. A coterminal angle to this could have which of the following measurements? Be sure to check all correct answers!
**Options:**
- A) 133°
- B) 947°
- C) -853°
- D) -47°
- E) 3827°
- F) 587°
**Explanation:**
To find coterminal angles, you can add or subtract full rotations (360 degrees) from the given angle. For a given angle θ, coterminal angles can be found using the formula:
θ + 360n
where n is any integer (positive, negative, or zero).
Let's determine if each of these options is coterminal with 227 degrees.
- **A) 133°**
\[
227° - 360° = -133°
\]
Since -133° is different from 133°, this is not a correct answer.
- **B) 947°**
\[
947° - 360° \times 2 = 227°
\]
Since 947° is coterminal with 227°, this is a correct answer.
- **C) -853°**
\[
-853° + 360° \times 3 = 227°
\]
Since -853° is coterminal with 227°, this is a correct answer.
- **D) -47°**
\[
-47° + 360° \times 1 = 313°
\]
Since 313° is different from 227°, this is not a correct answer.
- **E) 3827°**
\[
3827° - 360° \times 10 = 227°
\]
Since 3827° is coterminal with 227°, this is a correct answer.
- **F) 587°**
\[
587° - 360° = 227°
\]
Since 587° is coterminal with 227°, this is a correct answer.
Therefore, the correct answers are B) 947°, C) -853°, E) 3827°, and F) 587°.
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