Question

The time is 2:46 PM. What is the measure of the angle that the minute hand swept through since 2:00 PM?

Answer 1

The minute hand has swept through 46 minutes on the clock. You have to set up a ratio to solve this:

$\frac{46\ minutes}{60\ minutes} = \frac{x\ degrees}{360\ degrees}$

You can compare the 60 minutes on a clock to 360 degrees because 60 minutes on a clock is one whole rotation. So then, you cross multiply and simplify:

$\frac{46\ minutes}{60\ minutes} = \frac{x\ degrees}{360\ degrees}\\\\46*360=x*60\\16560=60x\\276=x$

Therefore, the minute hand has swept through an angle with a measure of 276 degrees.