Find The Degree Measure Of The Angle Created By The Given Part Of A Circle, 1 10 \frac{1}{10} 10 1 Of A Circle.A. 36 ∘ 36^{\circ} 3 6 ∘ B. 30 ∘ 30^{\circ} 3 0 ∘ C. 40 ∘ 40^{\circ} 4 0 ∘ D. 18 ∘ 18^{\circ} 1 8 ∘

Mar 11, 2025 by ADMIN 213 views

**Finding the Degree Measure of an Angle in a Circle**

Understanding the Problem

When dealing with circles, it's essential to understand the relationship between the angle and the fraction of the circle it represents. In this problem, we're given a fraction of a circle, $\frac{1}{10}$ , and we need to find the degree measure of the angle created by this fraction.

The Relationship Between Angles and Fractions of a Circle

A full circle has a total of 360 degrees. When we divide a circle into equal parts, each part represents a fraction of the total circle. In this case, we're dealing with a fraction of $\frac{1}{10}$ , which means we're looking at one-tenth of the total circle.

Calculating the Angle Measure

To find the degree measure of the angle created by this fraction, we can use the following formula:

Angle Measure = (Fraction of Circle) x (Total Degrees in a Circle)

In this case, the fraction of the circle is $\frac{1}{10}$ , and the total degrees in a circle is 360.

Applying the Formula

Let's plug in the values into the formula:

Angle Measure = ( $\frac{1}{10}$ ) x 360

To solve for the angle measure, we can multiply the fraction by the total degrees:

Angle Measure = 36

Evaluating the Answer Choices

Now that we have the angle measure, let's evaluate the answer choices:

A. $36^{\circ}$

B. $30^{\circ}$

C. $40^{\circ}$

D. $18^{\circ}$

Based on our calculation, the correct answer is:

A. $36^{\circ}$

Conclusion

In this problem, we used the relationship between angles and fractions of a circle to find the degree measure of the angle created by a given fraction of a circle. By applying the formula and evaluating the answer choices, we determined that the correct answer is $36^{\circ}$ .

Additional Examples

To further illustrate this concept, let's consider a few more examples:

If we have a fraction of $\frac{1}{4}$ of a circle, what is the degree measure of the angle created by this fraction?
If we have a fraction of $\frac{3}{5}$ of a circle, what is the degree measure of the angle created by this fraction?

Solving the First Example

To solve the first example, we can use the same formula:

Angle Measure = (Fraction of Circle) x (Total Degrees in a Circle)

In this case, the fraction of the circle is $\frac{1}{4}$ , and the total degrees in a circle is 360.

Angle Measure = ( $\frac{1}{4}$ ) x 360

To solve for the angle measure, we can multiply the fraction by the total degrees:

Angle Measure = 90

Solving the Second Example

To solve the second example, we can use the same formula:

Angle Measure = (Fraction of Circle) x (Total Degrees in a Circle)

In this case, the fraction of the circle is $\frac{3}{5}$ , and the total degrees in a circle is 360.

Angle Measure = ( $\frac{3}{5}$ ) x 360

To solve for the angle measure, we can multiply the fraction by the total degrees:

Angle Measure = 216

Conclusion

Q: What is the relationship between angles and fractions of a circle?

A: The relationship between angles and fractions of a circle is that each fraction of the circle represents a corresponding angle measure. When we divide a circle into equal parts, each part represents a fraction of the total circle, and each fraction corresponds to a specific angle measure.

Q: How do I calculate the angle measure of a fraction of a circle?

A: To calculate the angle measure of a fraction of a circle, you can use the following formula:

Angle Measure = (Fraction of Circle) x (Total Degrees in a Circle)

For example, if we have a fraction of $\frac{1}{10}$ of a circle, the angle measure would be:

Angle Measure = ( $\frac{1}{10}$ ) x 360 = 36

Q: What if I have a fraction with a denominator other than 10?

A: If you have a fraction with a denominator other than 10, you can still use the formula to calculate the angle measure. For example, if we have a fraction of $\frac{3}{5}$ of a circle, the angle measure would be:

Angle Measure = ( $\frac{3}{5}$ ) x 360 = 216

Q: Can I use this formula to find the angle measure of a fraction of a circle that is greater than 1?

A: Yes, you can use this formula to find the angle measure of a fraction of a circle that is greater than 1. For example, if we have a fraction of $\frac{3}{2}$ of a circle, the angle measure would be:

Angle Measure = ( $\frac{3}{2}$ ) x 360 = 540

Q: What if I have a fraction of a circle that is less than 1?

A: If you have a fraction of a circle that is less than 1, you can still use the formula to calculate the angle measure. For example, if we have a fraction of $\frac{1}{5}$ of a circle, the angle measure would be:

Angle Measure = ( $\frac{1}{5}$ ) x 360 = 72

Q: Can I use this formula to find the angle measure of a fraction of a circle that is a decimal?

A: Yes, you can use this formula to find the angle measure of a fraction of a circle that is a decimal. For example, if we have a fraction of 0.25 of a circle, the angle measure would be:

Angle Measure = 0.25 x 360 = 90

Q: What if I have a fraction of a circle that is a mixed number?

A: If you have a fraction of a circle that is a mixed number, you can convert it to an improper fraction and then use the formula to calculate the angle measure. For example, if we have a fraction of 2 $\frac{1}{4}$ of a circle, we can convert it to an improper fraction as follows:

2 $\frac{1}{4}$ = $\frac{9}{4}$

Then, we can use the formula to calculate the angle measure:

Angle Measure = ( $\frac{9}{4}$ ) x 360 = 810

Conclusion

In this article, we answered some frequently asked questions about angles and fractions of a circle. We provided examples and explanations to help you understand the relationship between angles and fractions of a circle and how to calculate the angle measure of a fraction of a circle using the formula. By understanding this relationship, you can solve a variety of problems involving angles and fractions of a circle.