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Since we know it is a cyclic quad, Angle A + Angle C is 180. 

So we can plug in angle A as 180- angle C. 

(180-angleC)/2  is equal to angleC/4

3 angle C is 360. 

Angle C is 120. So Angle A is 180-120 or 60. 

Now Angle B is 30*3 or 90. So Angle D is 180-90 or 90. 

The largest angle out of all of these are angle C or 120.

Hope this helps. 

~~GF

∠A            ∠C      

___  =     ____       wihich implies  that  

   2             4

4∠A  = 2∠C       which implies that

2∠A    =  ∠C

But  ∠A  + ∠C   are supplementary......so....

∠A + 2∠A  = 180°

3∠A  = 180°

∠A  =60°

So  ∠C = 2∠A  =  2(60)  =120°

Further we have that

∠B           ∠C           120

___  =     ____  =   ____   =   30

  3              4             4

So

∠B

___  =   30

  3

∠B  = 90

And   ∠B  + ∠D   are supplementary

So

∠B   + ∠D   = 180

90  + ∠D  = 180

∠D  =90°

So  C is the largest angle  = 120°

Thanks to both goreisthebest and CphIll!