The angles of a hexagon are in the ratio $1:2:3:4:5:5$. The largest angle is:

The angles of a hexagon are in the ratio $1:2:3:4:5:5$. The largest angle is:
  1. $120^{\circ}$
  2. $150^{\circ}$
  3. $180^{\circ}$
  4. $200^{\circ}$

Solution

Sum $= 720^{\circ}$. Let the angles be $x, 2x, 3x, 4x, 5x, 5x$. Then $20x = 720 \Rightarrow x = 36^{\circ}$. Largest $= 5x = 180^{\circ}$.

Asked in: IMO

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