Answer :
The measure of the inscribed Angle ACB is (31/360) × πr
Inscribed angles and central angles are two different kinds of angles in a circle. Both angles share the same vertex and endpoints, but their position differs.
Inscribed angles are the angles formed from two intersecting chords in a circle, whereas central angles are the angles whose vertex is the center of the circle and whose endpoints lie on the circle. These two kinds of angles have a special relationship, which can be explained using the Central Angle Theorem.
Let's look at how to use the Central Angle Theorem to solve this problem. Here is the diagram of the given problem: Inscribed Angle and Central Angle
The Central Angle Theorem states that the measure of a central angle is twice the measure of its corresponding inscribed angle. It means that if you know the measure of a central angle, you can find the measure of the inscribed angle. The inscribed angle and the central angle both have the same intercepted arc, so the measure of the inscribed angle is half the measure of the intercepted arc.
To find the measure of the inscribed angle ACB, we need to find the measure of the intercepted arc AB first. Using the formula for finding the measure of an arc, which is: measure of arc = (central angle/360) × 2πrWe can find the measure of the intercepted arc AB as follows:
measure of arc AB = (62/360) × 2πr Note that we don't know the radius of the circle, so we can't find the exact measure of the arc. However, we don't need to know the exact measure of the arc to find the measure of the inscribed angle. We only need to know that the measure of the arc is twice the measure of the inscribed angle ACB. Therefore, we can write: measure of inscribed angle ACB = (1/2) × (measure of arc AB)measure of inscribed angle ACB = (1/2) × (62/360) × 2πrSimplifying this expression, we get: measure of inscribed angle ACB = (31/360) × πr
Hence, the measure of the inscribed angle ACB is (31/360) × πr.
For more questions on Angle .
https://brainly.com/question/30759856
#SPJ8
