An angle in a circle whose vertex is at the center of the circle is called a __ angle. ANSWER: CENTRAL
The Correct Answer and Explanation is:
An angle in a circle whose vertex is at the center of the circle is called a central angle.
A central angle is formed when two radii of a circle are drawn from the center to the circle’s boundary. The angle between these two radii is called the central angle. The measure of this angle is directly proportional to the arc it subtends (the part of the circle’s circumference between the two points where the radii meet the boundary). The central angle essentially divides the circle into sectors, with each sector having an angle at the center.
The key property of a central angle is that its degree measure is equal to the measure of the arc it intercepts. For example, if a central angle measures 60°, the arc between the two points where the radii meet the circumference will also measure 60°. This relationship helps in calculations of lengths of arcs and areas of sectors, where knowledge of central angles is essential. Additionally, if the central angle covers the entire circumference of the circle, its measure will be 360°, completing a full circle.
Central angles are used in various geometry problems, including finding the area of sectors and arcs, and they are foundational in understanding how angles work within circles. The relationship between central angles and inscribed angles (angles formed by points on the circle’s circumference) is also significant in circle geometry, as the measure of an inscribed angle is half of the corresponding central angle that subtends the same arc.
