A circle has a circumference of 10 it has an arc length of nine over two what is a central angle of the ark in degrees

Answer 1

This is a ratio question. We can find the central angle by comparing it to the length of the arc.

From the problem, we know the circle has a circumference of 10. We also know a circle is 360°. We know the arc has a length of 9/2, or 4.5, and we need to determine the number of degrees for the central angle of the arc. To solve, we need to set up a ratio where the angle is the unknown, let's call it x.

length of the arc / circumference = angle of the arc / angle of the circle

4.5 / 10 = x / 360

multiplying both sides by 360 we get:

(4.5 x 360) / 10 = x

162 = x

Therefore, the central angle is 162°.

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