In a circle, the measure of an inscribed angle is one-half the measure of its intercepted arc.
Is this true or false?
The measure of an interior angle is one half of the measure of the intercepted arc.
This statement is true. To understand why, we need to consider the relationship between inscribed angles and intercepted arcs in a circle.
An inscribed angle is an angle formed by two intersecting chords or tangents inside a circle. The intercepted arc refers to the arc of the circle between the two endpoints of the inscribed angle.
In a circle, we can draw a central angle that subtends the same arc as the inscribed angle. The central angle is formed by two radii that extend from the center of the circle to the endpoints of the intercepted arc.
Now, let's look at the relationship between the measure of an inscribed angle and its intercepted arc.
According to the Inscribed Angle Theorem, the measure of an inscribed angle is equal to half the measure of its intercepted arc. This means that if an inscribed angle cuts off an arc with a measure of x degrees, the measure of the inscribed angle will be x/2 degrees.
Therefore, the statement "In a circle, the measure of an inscribed angle is one-half the measure of its intercepted arc" is true.