A circle is a curve sketched out by a point moving in a plane. The measure of the central angle of a circle with radius 60 centimeters that intercepts a 15π centimeters arc is 45°.
What is a circle?
A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given a circle with radius 60 centimeters that intercepts a 15π centimeters arc on the circle. Now, the measure of the central angle of the arc can be written as,
Length of water = 2πr × (θ/360°)
15 π = 2 × π × 60 × (θ/360°)
15 × 360/ 2 × 60 = θ
θ = 45°
Hence, the measure of the central angle of a circle with radius 60 centimeters that intercepts a 15π centimeters arc is 45°.
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