One quick geometry question. I have the answer, but I need the work. It's a test correction and I don't understand how to solve it.

Question

annipuppi · Answer

The answer is 27

annipuppi · Answer

@surjithayer @ganeshie8 please, I really need help on this. I've tried so many ways of solving it, but I can't come up with the right answer... how do I do it?

ganeshie8 · Answer

http://www.regentsprep.org/Regents/math/geometry/GP15/CircleAngles.htm scroll down to the last

annipuppi · Answer

THANK YOU! so u=1/2(120-66)
u=1/2(54)
u=27?

ganeshie8 · Answer

since the inscribed angle $\angle S = 33$,
near arc = $33\times 2 = 66$


apply the formula :
$\angle U = \dfrac{\text{(far arc) - (near arc)}}{2} = \dfrac{120-66}{2} = 27$

annipuppi · Answer

Okay, thank you so much!

ganeshie8 · Answer

yw