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°