# Intermediate Geometry : How to find the angle of a sector

## Example Questions

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### Example Question #1 : How To Find The Angle Of A Sector

In the circle above, the length of arc BC is 100 degrees, and the segment AC is a diameter. What is the measure of angle ADB in degrees?

cannot be determined

80

100

40

90

40

Explanation:

Since we know that segment AC is a diameter, this means that the length of the arc ABC must be 180 degrees. This means that the length of the arc AB must be 80 degrees.

Since angle ADB is an inscribed angle, its measure is equal to half of the measure of the angle of the arc that it intercepts. This means that the measure of the angle is half of 80 degrees, or 40 degrees.

### Example Question #1 : How To Find The Angle Of A Sector

What is the angle of a sector of area   on a circle having a radius of ?

Explanation:

To begin, you should compute the complete area of the circle:

Now, to find the angle measure of a sector, you find what portion of the circle the sector is. Here, it is:

Now, multiply this by the total  degrees in a circle:

Rounded, this is .

### Example Question #7 : How To Find The Angle Of A Sector

What is the angle of a sector that has an arc length of   on a circle of diameter  ?

Explanation:

The first thing to do for this problem is to compute the total circumference of the circle. Notice that you were given the diameter. The proper equation is therefore:

Now, to compute the angle, note that you have a percentage of the total circumference, based upon your arc length:

Rounded to the nearest hundredth, this is .

### Example Question #1 : How To Find The Angle Of A Sector

What is the sector angle, in degrees, if the area of the sector is  with a given radius of ?

Explanation:

Write the formula for the area of a circular sector.

Substitute the given information and solve for theta:

### Example Question #2 : How To Find The Angle Of A Sector

The length of the intercepted arc of a sector of a circle with radius  meters is  meters.  Find the measure of the central angle of the sector.

Explanation:

The formula for the length of an arc is

where  is measure of the central angle and  is the radius.  Substituting what we know gives.

Therefore, our central angle has a measure of

### Example Question #3 : How To Find The Angle Of A Sector

A sector in a circle with a radius of  has an area of . In degrees, what is the measurement of the central angle for this sector?

Explanation:

Recall how to find the area of a sector:

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

Plug in the given information to find the measurement of the central angle.

The central angle is  degrees.

### Example Question #4 : How To Find The Angle Of A Sector

A sector in a circle with a radius of  has an area of . In degrees, what is the measurement of the central angle of the sector?

Explanation:

Recall how to find the area of a sector:

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

Plug in the given information to find the measurement of the central angle.

The central angle is  degrees.

### Example Question #5 : How To Find The Angle Of A Sector

A sector in a circle with a radius of  has an area of . In degrees, what is the measurement of the central angle of the sector?

Explanation:

Recall how to find the area of a sector:

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

Plug in the given information to find the measurement of the central angle.

The central angle is  degrees.

### Example Question #6 : How To Find The Angle Of A Sector

A sector in a circle with a radius of  has an area of . In degrees, what is the measurement of the central angle in the sector?

Explanation:

Recall how to find the area of a sector:

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

Plug in the given information to find the measurement of the central angle.

The central angle is  degrees.

### Example Question #7 : How To Find The Angle Of A Sector

A sector in a circle with a radius of  has an area of . In degrees, what is the measurement of the central angle of the sector?

Explanation:

Recall how to find the area of a sector:

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

Plug in the given information to find the measurement of the central angle.

The central angle is  degrees.

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