Point C is the center of the circle. Angle ACB measures56 degrees What is the measure of arc AB?
How do you work this out?
You have to know the radius.
Suppose the radius is r, then your arc AB
= (56/360)(2πr)
To determine the measure of arc AB, you can use the fact that the measure of an inscribed angle is half the measure of its intercepted arc. In this case, angle ACB measures 56 degrees.
So, the measure of arc AB would be twice that of angle ACB, or 2 * 56 = 112 degrees.
To find the measure of arc AB, you need to use the fact that angles inscribed in the same arc are congruent. Therefore, since angle ACB measures 56 degrees, arc AB will also measure 56 degrees.
To work it out geometrically, draw a circle with point C as the center. Angle ACB is an angle formed by two radii (lines drawn from the center of the circle to a point on the circle) intercepting an arc AB. Since angle ACB measures 56 degrees, arc AB will also measure 56 degrees.
Alternatively, you can also use the formula for finding the measure of a circle's arc when given the measure of the corresponding central angle. The formula is:
Measure of arc = (Angle measure / 360 degrees) * Circumference of the circle.
In this case, the angle measure is 56 degrees and since point C is the center of the circle, the circumference of the circle will be the entire circumference. Therefore, the measure of arc AB can be calculated as:
Measure of arc AB = (56 degrees / 360 degrees) * Circumference of the circle.
Since the entire circumference is not given in the question, it cannot be calculated directly. But if the radius or diameter of the circle is provided, the circumference can be calculated using the formulas:
Circumference = 2 * π * radius,
or
Circumference = π * diameter.
Once you know the circumference, you can substitute it into the formula above to find the measure of arc AB.