All Intermediate Geometry Resources
Example Questions
Example Question #1 :如何找到一个行业的角度
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?
40
cannot be determined
90
80
100
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 #8 :如何找到一个行业的角度
What is the angle of a sector of areaon a circle having a radius of?
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 totaldegrees in a circle:
Rounded, this is.
Example Question #1 :如何找到一个行业的角度
What is the angle of a sector that has an arc length ofon a circle of diameter?
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.
Example Question #1 :如何找到一个行业的角度
What is the sector angle, in degrees, if the area of the sector iswith a given radius of?
Write the formula for the area of a circular sector.
Substitute the given information and solve for theta:
Example Question #2 :如何找到一个行业的角度
The length of the intercepted arc of a sector of a circle with radiusmeters ismeters. Find the measure of the central angle of the sector.
The formula for the length of an arc is
whereis measure of the central angle andis the radius. Substituting what we know gives.
Therefore, our central angle has a measure of
Example Question #3 :如何找到一个行业的角度
A sector in a circle with a radius ofhas an area of. In degrees, what is the measurement of the central angle for this sector?
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 isdegrees.
Example Question #4 :如何找到一个行业的角度
A sector in a circle with a radius ofhas an area of. In degrees, what is the measurement of the central angle of the sector?
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 isdegrees.
Example Question #5 :如何找到一个行业的角度
A sector in a circle with a radius ofhas an area of. In degrees, what is the measurement of the central angle of the sector?
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 isdegrees.
Example Question #6 :如何找到一个行业的角度
A sector in a circle with a radius ofhas an area of. In degrees, what is the measurement of the central angle in the sector?
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 isdegrees.
Example Question #7 :如何找到一个行业的角度
A sector in a circle with a radius ofhas an area of. In degrees, what is the measurement of the central angle of the sector?
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 isdegrees.