Theorem 12-4
Relationship between arcs and central angles
In a circle, the measure of a central angle is equal to the measure of its intercepted arc. Similarly, the measure of an intercepted arc is equal to the measure of the central angle that subtends it.
Theorem 12-4 states the relationship between arcs and central angles in a circle.
According to the theorem, the measure of a central angle in a circle is equal to the measure of its intercepted arc. In other words, if you have a central angle with a measure of x degrees, the intercepted arc by that angle will also have a measure of x degrees.
Conversely, if you have an arc in a circle with a measure of x degrees, the central angle that intercepts that arc will also have a measure of x degrees.
This theorem is useful in geometry and trigonometry when dealing with circles and angles. It helps establish the relationship between the measures of angles and arcs within a circle.