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Central angle
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Does a central angle and its intercepted arc have the same measure?
yes or true
If a central angle measures 87 and deg then its arc will measure .?
The same as the central angle of the circle
Is the measure of an arc congruent to the measure of its central angle?
No.
How do you find the arc length with the angle given?
An arc can be measured either in degree or in unit length. An arc is a portion of the circumference of the circle which is determined by the size of its corresponding central angle. We create a proportion that compares the arc to the whole circle first in degree measure and then in unit length. (measure of central angle/360 degrees) = (arc length/circumference) arc length = (measure of central angle/360 degrees)(circumference) But, maybe the angle that determines the arc in your problem is not a central angle. In such a case, find the arc measure in degree, and then write the proportion to find the arc length.
If the measure of a tangent chord angle is 54 then what is the measure of the intercepted arc inside the angle?
108
Does a central angle and its intercepted arc have the same measure?
yes or true
If a central angle measures 87 and deg then its arc will measure .?
The same as the central angle of the circle
What is the difference between the measure of an arc and arc length?
They are normally the same. However, the measure of the arc could refer to the angle subtended at the centre of the radius of curvature.
What is a congruent arc?
Congruent arcs are circle segments that have the same angle measure and are in the same or congruent circles.
Is it true or false that the measure of a tangent-chord angle is twice the measure of the intercepted arc inside the angle?
It is true that the measure of a tangent-chord angle is half the measure of the intercepted arc inside the angle. When a tangent line intersects a chord of a circle, it creates an angle between the tangent line and the chord, known as the tangent-chord angle. If we draw a segment from the center of the circle to the midpoint of the chord, it will bisect the chord, and the tangent-chord angle will be formed by two smaller angles, one at each end of this segment. Now, the intercepted arc inside the tangent-chord angle is the arc that lies between the endpoints of the chord and is inside the angle. The measure of this arc is half the measure of the central angle that subtends the same arc, which is equal to the measure of the angle formed by the two smaller angles at the ends of the segment that bisects the chord. Therefore, we can conclude that the measure of a tangent-chord angle is half the measure of the intercepted arc inside the angle.
If the arc on a particular circle has an arc length of 12 inches and the circumference of the circle is 48 inches what is the angle measure of the arc?
The angle measure is: 90.01 degrees
Is the measure of an arc congruent to the measure of its central angle?
No.
How do you find measure of minor arc?
the measure of a minor arc equals the measure of the central angle that intercepts it.
How is the length of an arc different from the measure of an arc?
measure= same as central angle, in degrees length= like line straightened out, measured in inches, meters, feet, etc.
If the measure of a tangent angle is 36 then what is the measure of the intercepted arc inside the angle?
72
How do you find the arc length with the angle given?
An arc can be measured either in degree or in unit length. An arc is a portion of the circumference of the circle which is determined by the size of its corresponding central angle. We create a proportion that compares the arc to the whole circle first in degree measure and then in unit length. (measure of central angle/360 degrees) = (arc length/circumference) arc length = (measure of central angle/360 degrees)(circumference) But, maybe the angle that determines the arc in your problem is not a central angle. In such a case, find the arc measure in degree, and then write the proportion to find the arc length.
Is the measure of an arc equal to the measure of its central angle?
Yes. Besides the included angle, arc length is also dependant on the radius. Arc length = (Pi/180) x radius x included angle in degrees.
