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Intercepted arc I believe
360 degree
In a circle what is the difference between a central angle and an arc?Read more: In_a_circle_what_is_the_difference_between_a_central_angle_and_an_arc
The relation between the arc of length and the central angle is that the arc of length divided by one of the sides is the central angle in radians. If the arc is a full circle, then the central angle is 2pi radians or 360 degrees.
72
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.
yes or true
If the radius of a circle is tripled, how is the length of the arc intercepted by a fixed central angle changed?
Intercepted arc I believe
A sector is the area enclosed by two radii of a circle and their intercepted arc, and the angle that is formed by these radii, is called a central angle. A central angle is measured by its intercepted arc. It has the same number of degrees as the arc it intercepts. For example, a central angle which is a right angle intercepts a 90 degrees arc; a 30 degrees central angle intercepts a 30 degrees arc, and a central angle which is a straight angle intercepts a semicircle of 180 degrees. Whereas, an inscribed angle is an angle whose vertex is on the circle and whose sides are chords. An inscribed angle is also measured by its intercepted arc. But, it has one half of the number of degrees of the arc it intercepts. For example, an inscribed angle which is a right angle intercepts a 180 degrees arc. So, we can say that an angle inscribed in a semicircle is a right angle; a 30 degrees inscribed angle intercepts a 60 degrees arc. In the same or congruent circles, congruent inscribed angles have congruent intercepted arcs.
360 degree
-- Circumference of the circle = (pi) x (radius) -- length of the intercepted arc/circumference = degree measure of the central angle/360 degrees
The interior angle and central angle are supplementary, that is they always add up to 180 degrees, while the exterior angle and the central angle will always be the same.
Central angle of a circle is the same as the measure of the intercepted arc. davids1: more importantly the formulae for a central angle is π=pi, R=radius Central Angle= Arc Length x 180 / π x R
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.
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.
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.