64°/360° = 8/45 of the circle = 0.1777 (rounded, repeating)
The arc's length is 8/45 of the circle's total circumference.
Examples to show how to use the property that the measure of a central angle is equal to the measure of its intercepted arc to find the missing measures of arcs and angles in given figures.
87 degrees
102.8 degrees I think but it depends. If the angle is a central angle it is 51.4 degrees but other than that I think it would be 102.8 degrees.
In a circle, a central angle is formed by two radii. By definition, the measure of the intercepted arc is equal to the central angle.
A central angle is measured by its intercepted arc. Let's denote the length of the intercepted arc with s, and the length of the radius r. So, s = 6 cm and r = 30 cm. When a central angle intercepts an arc whose length measure equals the length measure of the radius of the circle, this central angle has a measure 1 radian. To find the angle in our problem we use the following relationship: measure of an angle in radians = (length of the intercepted arc)/(length of the radius) measure of our angle = s/r = 6/30 = 1/5 radians. Now, we need to convert this measure angle in radians to degrees. Since pi radians = 180 degrees, then 1 radians = 180/pi degrees, so: 1/5 radians = (1/5)(180/pi) degrees = 36/pi degrees, or approximate to 11.5 degrees.
360 degree
Examples to show how to use the property that the measure of a central angle is equal to the measure of its intercepted arc to find the missing measures of arcs and angles in given figures.
87 degrees
It is the measure of half the intercepted arc.
-- Circumference of the circle = (pi) x (radius) -- length of the intercepted arc/circumference = degree measure of the central angle/360 degrees
102.8 degrees I think but it depends. If the angle is a central angle it is 51.4 degrees but other than that I think it would be 102.8 degrees.
150
The answer is half the measure, 62°. Have a nice day!
60 degrees
In a circle, a central angle is formed by two radii. By definition, the measure of the intercepted arc is equal to the central angle.
A central angle is measured by its intercepted arc. Let's denote the length of the intercepted arc with s, and the length of the radius r. So, s = 6 cm and r = 30 cm. When a central angle intercepts an arc whose length measure equals the length measure of the radius of the circle, this central angle has a measure 1 radian. To find the angle in our problem we use the following relationship: measure of an angle in radians = (length of the intercepted arc)/(length of the radius) measure of our angle = s/r = 6/30 = 1/5 radians. Now, we need to convert this measure angle in radians to degrees. Since pi radians = 180 degrees, then 1 radians = 180/pi degrees, so: 1/5 radians = (1/5)(180/pi) degrees = 36/pi degrees, or approximate to 11.5 degrees.
yes or true