Two gears are connected and are rotating simultaneously. the smaller gear has a radius of 2 inches, and the larger gear has a radius of 8 inches.

two circles touching at one point. larger circle has radius of 8 inches. smaller circle has radius of 2 inches.

part 1: what is the angle measure, in degrees and rounded to the nearest tenth, through which the larger gear has rotated when the smaller gear has made one complete rotation?

part 2: how many rotations will the smaller gear make during one complete rotation of the larger gear?

R - radius of the larger circle
r - radius of the smaller circle

Circumference of the larger circle = 
Circumference of the smaller circle = 

Part 2:  During one complete rotation of the larger gear both gears pass the same distance .
Therefore, the smaller gear makes  complete rotations.

Part 1: During one complete rotation of the smaller gear both gears pass the same distance .
Therefore, the larger gear makes  of a complete rotation. 
Since one complete rotation corresponds to 360 degrees, 1/4 of a complete rotation corresponds to 360/4=90 degrees.