ACT Math : How to find the angle of a sector
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Example Questions
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?
90
cannot be determined
80
100
40
40
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 #2 : How To Find The Angle Of A Sector
What is the angle of a sector of area 
To begin, you should compute the complete area of the circle:
For your data, this is:
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 
Rounded, this is 
Example Question #3 : How To Find The Angle Of A Sector
What is the angle of a sector that has an arc length of 
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:
For your data, this means,
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 
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