Question

A circle is centered at the vertex of an angle, and the angle's rays subtend an arc that is 74.46 cm long. 1/360th of the circumference of the circle is 0.51 cm long. What is the measure of this angle in degrees?

________degrees
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Answer 1

146°

Explanation:

You're given an angle, where the vertex is the center of a circle. This makes the angle's rays two radii of the circle. You are then given the length of 1/360th of the circle, which is .51cm, which is also 1 degree of the circle.

If the arc of the circle between the angle's rays is 74.46 cm. It becomes a division problem:

`(74.46 cm)/(.51 cm)`

After the division, the fraction simplifies to 146, which is 146 segments of .51cm in the arc, and since .51cm is equivalent to 1 degree of the circle, the arc is 146 degrees.