Thank you for visiting Which of the following statements are true A An inscribed angle can be up to 360 degrees B The measure of an arc is equal. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The true statements are that the measure of an arc is equal to the measure of the central angle that intercepts it and a central angle can be up to 360 degrees. An inscribed angle cannot measure up to 360 degrees, and its measure is half that of the arc it intercepts.
The question concerns the properties of angles and arcs within circles in geometry. Let's address each of the statements provided:
- a. An inscribed angle can be up to 360 degrees: This is false. An inscribed angle, which is formed by two chords in a circle that meet at a common endpoint, cannot measure up to 360 degrees because it would then be a full circle itself, which is not an angle.
- b. The measure of an arc is equal to the measure of the central angle that intercepts it: This statement is true. In a circle, the arc's measure corresponds to the measure of the central angle that intercepts the arc, per the central angle theorem.
- c. The measure of an arc is equal to the measure of the inscribed angle that intercepts it: This is false. The measure of an inscribed angle is actually half the measure of the arc it intercepts.
- d. A central angle can be up to 360 degrees: This statement is true. A central angle is formed by two radii of a circle, and it can measure up to 360 degrees when the radii coincide to form a full circle.
To summarize further, arc length (As) is directly related to the central angle (A0) and the radius of the circle (r). The relationship between these elements is described mathematically by the equation A = As/r, which defines the measure in radians.
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Rewritten by : Jeany
