Quadrilateral in circle

A quadrilateral is inscribed in the circle so that its vertices divide the circle 1: 2: 3: 4. Find the sizes of its interior angles.

Correct answer:

A =  90 °
B =  126 °
C =  90 °
D =  54 °

Step-by-step explanation:

Φ1=ASB;Φ2=BSC;Φ3=CSD;Φ4=DSA  Φ1:Φ2:Φ3:Φ4=o1:o2:o3:o4=1:2:3:4  x=1+2+3+4360=36   Φ1=1 x=1 36=36  Φ2=2 x=2 36=72  Φ3=3 x=3 36=108  Φ4=4 x=4 36=144   A=2180Φ1+2180Φ4=218036+2180144=90
D=2180Φ3+2180Φ4=2180108+2180144=54=54   Verifying Solution:   s=A+B+C+D=90+126+90+54=360 

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