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
​

Answer 1

Answer:

146°

Step-by-step 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:

$\frac{74.46 cm}{.51 cm}$

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.