The minute hand has swept through 46 minutes on the clock. You have to set up a ratio to solve this:
[tex]\frac{46\ minutes}{60\ minutes} = \frac{x\ degrees}{360\ degrees}[/tex]
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:
[tex]\frac{46\ minutes}{60\ minutes} = \frac{x\ degrees}{360\ degrees}\\\\46*360=x*60\\16560=60x\\276=x[/tex]
Therefore, the minute hand has swept through an angle with a measure of 276 degrees.
