Select The Correct Answer.Which Angle Measure Less Than Or Equal To 360° Is Equivalent To An Angle Of 17°?A. 45°B. 135°C. 230°

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Introduction

In mathematics, angles are measured in degrees, and understanding the relationships between different angles is crucial for solving various problems. One such concept is finding an angle measure less than or equal to 360° that is equivalent to a given angle. In this article, we will explore how to find an angle measure less than or equal to 360° that is equivalent to an angle of 17°.

What are Equivalent Angles?

Equivalent angles are angles that have the same measure, but may be located in different positions or orientations. In other words, two angles are equivalent if they have the same degree measure, regardless of their position on the circle. For example, an angle of 17° is equivalent to an angle of 17° + 360°, which is 377°.

Finding Equivalent Angles

To find an angle measure less than or equal to 360° that is equivalent to an angle of 17°, we need to add or subtract multiples of 360° from the given angle. This is because the sum of the measures of two angles that form a straight line is always 180°, and the sum of the measures of two angles that form a full circle is always 360°.

Calculating Equivalent Angles

Let's calculate the equivalent angles for 17° by adding and subtracting multiples of 360°:

  • 17° + 360° = 377°
  • 17° + 2(360°) = 737°
  • 17° + 3(360°) = 1097°
  • 17° + 4(360°) = 1457°
  • 17° + 5(360°) = 1817°

We can also subtract multiples of 360° from 17° to find equivalent angles:

  • 17° - 360° = -343°
  • 17° - 2(360°) = -703°
  • 17° - 3(360°) = -1063°
  • 17° - 4(360°) = -1463°
  • 17° - 5(360°) = -1863°

Selecting the Correct Answer

Based on the calculations above, we can see that the angle measure less than or equal to 360° that is equivalent to an angle of 17° is 377°. Therefore, the correct answer is:

A. 45° is not correct, as it is not equivalent to 17°. B. 135° is not correct, as it is not equivalent to 17°. C. 230° is not correct, as it is not equivalent to 17°. D. 377° is the correct answer, as it is equivalent to 17°.

Conclusion

In conclusion, finding an angle measure less than or equal to 360° that is equivalent to a given angle requires understanding the concept of equivalent angles and how to calculate them by adding or subtracting multiples of 360°. By following the steps outlined in this article, you can determine the correct answer to this problem and develop a deeper understanding of angle equivalences in mathematics.

Additional Examples

Here are a few more examples of finding equivalent angles:

  • Find an angle measure less than or equal to 360° that is equivalent to an angle of 25°.
  • Find an angle measure less than or equal to 360° that is equivalent to an angle of 50°.
  • Find an angle measure less than or equal to 360° that is equivalent to an angle of 75°.

Solutions to Additional Examples

  • For an angle of 25°, the equivalent angles are:
    • 25° + 360° = 385°
    • 25° + 2(360°) = 725°
    • 25° + 3(360°) = 1065°
    • 25° + 4(360°) = 1405°
    • 25° + 5(360°) = 1745°
  • For an angle of 50°, the equivalent angles are:
    • 50° + 360° = 410°
    • 50° + 2(360°) = 770°
    • 50° + 3(360°) = 1130°
    • 50° + 4(360°) = 1490°
    • 50° + 5(360°) = 1850°
  • For an angle of 75°, the equivalent angles are:
    • 75° + 360° = 435°
    • 75° + 2(360°) = 795°
    • 75° + 3(360°) = 1155°
    • 75° + 4(360°) = 1515°
    • 75° + 5(360°) = 1875°
      Frequently Asked Questions (FAQs) about Equivalent Angles =============================================================

Q: What is an equivalent angle?

A: An equivalent angle is an angle that has the same measure as another angle, but may be located in a different position or orientation.

Q: How do I find an equivalent angle?

A: To find an equivalent angle, you can add or subtract multiples of 360° from the given angle. This is because the sum of the measures of two angles that form a straight line is always 180°, and the sum of the measures of two angles that form a full circle is always 360°.

Q: What are some examples of equivalent angles?

A: Here are a few examples of equivalent angles:

  • 17° is equivalent to 377° (17° + 360°)
  • 25° is equivalent to 385° (25° + 360°)
  • 50° is equivalent to 410° (50° + 360°)
  • 75° is equivalent to 435° (75° + 360°)

Q: Can I use negative numbers to find equivalent angles?

A: Yes, you can use negative numbers to find equivalent angles. For example, -17° is equivalent to 343° (-17° + 360°).

Q: How do I know which equivalent angle to choose?

A: When choosing an equivalent angle, you should select the one that is less than or equal to 360°. This is because the problem typically asks for an angle measure less than or equal to 360°.

Q: Can I use a calculator to find equivalent angles?

A: Yes, you can use a calculator to find equivalent angles. However, it's always a good idea to understand the concept behind finding equivalent angles, as this will help you to solve problems more efficiently.

Q: What are some real-world applications of equivalent angles?

A: Equivalent angles have many real-world applications, including:

  • Architecture: Architects use equivalent angles to design buildings and structures that are aesthetically pleasing and functional.
  • Engineering: Engineers use equivalent angles to design machines and mechanisms that are efficient and effective.
  • Art: Artists use equivalent angles to create visually appealing compositions and designs.

Q: Can I use equivalent angles to solve trigonometry problems?

A: Yes, you can use equivalent angles to solve trigonometry problems. Trigonometry involves the study of triangles and the relationships between their sides and angles. Equivalent angles can be used to simplify trigonometric expressions and solve problems.

Q: What are some common mistakes to avoid when finding equivalent angles?

A: Here are some common mistakes to avoid when finding equivalent angles:

  • Not understanding the concept of equivalent angles
  • Not using the correct formula to find equivalent angles
  • Not selecting the correct equivalent angle
  • Not checking the answer for accuracy

Conclusion

In conclusion, equivalent angles are an important concept in mathematics that has many real-world applications. By understanding how to find equivalent angles, you can solve problems more efficiently and effectively. Remember to always choose the equivalent angle that is less than or equal to 360°, and to check your answer for accuracy.