Arcs
Part 1
We have and angle (85°) and a circle, both disposed as the following figure:
We want to find the measure of the blue segment. We know that a centered angle's ray corresponds to the same angle. Since each angle is 1/360th of the circumference, then the arc is 85 times one of those angles.
Then, we have the answer:
If a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is 85 times as long as 1/360th of the circumference of the circle.
Part B
Having the same graphic representation as before, in this case, we know that each 1/360th of the circumference is 0.06 cm long, since the arc is 85 times as long, then its lenght is
85 x 0.06 cm = 5.1 cm
What is the length of the arc subtended by the angle's rays? 5.1 cm