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How to Find Central Angle of a Circle?

TopThe central angle of a circle is the angle based at the circle's center. Here, we will discuss how to find the central angle of a circle. 

Given below are the steps for finding the central angle of a circle:

Step 1: First of all, we will calculate the circumference by using the following formula:
Circumference (C) = $2 \times \pi \times r$. Here, $\pi$ = 3.14 and ‘r’ is the radius, which is given in question. If diameter is given in diameter form, then we convert diameter into radius by dividing diameter by 2.

Step 2: After evaluation of circumference, now we calculate arc length of circle by using following formula:
Arc length (s) = $r \times \theta$

Step 3: After first two steps, now we calculate central angle of circle by using following formula:

Central angle of circle ($\theta$) = $\frac{\text{arc length} \times 360}{2 \times \pi \times r}$.

Now, we take an example to understand the process of evaluating the central angle of circle:

Example: Find the central angle of circle, whose arc length is 7.33 meter and diameter is 14 meter.

Solution: We use the following steps for evaluating a central angle of circle, whose diameter and arc length is given.

Step 1: First of all, we calculate circumference of circle by following formula:

Circumference (C) = $2 \times \pi \times r$

                           = $2 \times 3.14 \times ($$\frac{14}{2}$$)$. Here, 14 is diameter. So, radius is ($\frac{\text{Diameter}}{2}$),

                           = 2 x 3.14 x 7,

                           = 43.96 inches.

Step 2: Here, Arc Length of Circle is given.

Arc length (s) = 7.33 inches

Step 3: Now, we calculate central angle of circle by using the following formula:

Central angle of circle ($\theta$) = $\frac{\text{arc length} \times 360}{2 \times \pi \times r}$

                                               = $\frac{7.33 \times 360}{43.96}$

                                               = 60 degree

So, central angle of circle is '60 degree'.