Let's pick one person at random and call it the 'first'.
That person shakes hands with 29 other classmates.
Take another person different from the first, we'll call him the 'second'. Since he has already shaken hands with the first, he shakes hands with 28 other classmates.
The 'third' person will likewise shake hands with 27 other classmates, and so on.
Hence, the total number of handshakes is 29+28+27+...+2+1 = 29*30/2=435 handshakes
Solution:
we are given that
Inscribed angle![=(2.5x+4)](https://tex.z-dn.net/?f=%20%3D%282.5x%2B4%29%20)
Intercepted arc![=(7x-2)](https://tex.z-dn.net/?f=%20%3D%287x-2%29%20)
As we know that the Inscribed angle is Half of the measure of the intercepted arc.
So we can write
![(2.5x+4)=\frac{1}{2}(7x-2) \\\\7x-2=2(2.5x+4)\\\\7x-2=5x+8\\\\7x-5x=8+2\\\\2x=10\\\\x=5\\\\\text{So Measure of arc AC}=(7x-2)=7*5-2=35-2=33](https://tex.z-dn.net/?f=%20%282.5x%2B4%29%3D%5Cfrac%7B1%7D%7B2%7D%287x-2%29%20%5C%5C%5C%5C7x-2%3D2%282.5x%2B4%29%5C%5C%5C%5C7x-2%3D5x%2B8%5C%5C%5C%5C7x-5x%3D8%2B2%5C%5C%5C%5C2x%3D10%5C%5C%5C%5Cx%3D5%5C%5C%5C%5C%5Ctext%7BSo%20Measure%20of%20arc%20AC%7D%3D%287x-2%29%3D7%2A5-2%3D35-2%3D33%20)
$12.89 should be the answer bc 4.5+2.25=6.75 and 87 divided by 6.75 is 12.888888 so i would either round up or down