If the intercepted arc is twice the size of the inscribed angle, then the inscribed angle is half the size of the intercepted arc. So if the intercepted arc is 130 degrees, the inscribed angle is 130 / 2 = 65 degrees.
This statement is known as the "Arc Angle Theorem" or "Intercepted Arc Theorem". It states that an arc intercepted by an inscribed angle in a circle has a measure equal to twice the measure of the inscribed angle.
Formally, if an angle with vertex on a circle intercepts an arc of measure $\theta$, then the measure of the inscribed angle is half of the measure of the intercepted arc, i.e., $\angle ABC = \frac{1}{2}\theta$, where $\angle ABC$ is the inscribed angle and $\theta$ is the measure of the intercepted arc.
This theorem can be proven using the properties of angles formed by chords and tangents in a circle.
Answers & Comments
Answer:
False
Step-by-step explanation:
If the intercepted arc is twice the size of the inscribed angle, then the inscribed angle is half the size of the intercepted arc. So if the intercepted arc is 130 degrees, the inscribed angle is 130 / 2 = 65 degrees.
Verified answer
Answer:
True.
Step-by-step explanation:
This statement is known as the "Arc Angle Theorem" or "Intercepted Arc Theorem". It states that an arc intercepted by an inscribed angle in a circle has a measure equal to twice the measure of the inscribed angle.
Formally, if an angle with vertex on a circle intercepts an arc of measure $\theta$, then the measure of the inscribed angle is half of the measure of the intercepted arc, i.e., $\angle ABC = \frac{1}{2}\theta$, where $\angle ABC$ is the inscribed angle and $\theta$ is the measure of the intercepted arc.
This theorem can be proven using the properties of angles formed by chords and tangents in a circle.