Answer:
The sector for 126 rubies would measure 126 degrees.
Step-by-step explanation:
First, a pie-chart is a circle, and there are 360 degrees in a circle. Because there are 320 total gemstones, 1 gemstone maps to 1.125 degrees. That is, 1.125 degrees per gemstone.
[tex]360\div320=1.125[/tex]
Knowing that, you can calculate the degrees in the pie-chart for any given number of gemstones. Just multiply the gemstones by 1.125.
[tex]112\times1.125=126[/tex]
The sector for 112 rubies would measure 126 degrees.
If you want to be extra sure, you can calculate that for all types of gemstones and add them up:
[tex]32\times1.125=36\\112\times1.125=126\\96\times1.125=108\\64\times1.125=72\\16\times1.125=18\\36+126+108+72+18=360[/tex]
That confirms they all add up to 360 degrees.
