The angles of a cyclic quadrilateral are in the ratio 1:3:4:4. What is the measure of the largest angle?

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Accepted Answer

1. Let the common factor be $k$. The angles are $k,3k,4k,4k$.  
2. Sum of angles in a quadrilateral is $360^\circ$, so $k+3k+4k+4k=12k=360^\circ$.  
3. Solve: $k=30^\circ$.  
4. Largest angle $=4k=4	imes30^\circ=120^\circ$.  
FINAL_ANSWER: c

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