The angles of a quadrilateral are $(x), (x+10), (x+20)$ and $(x+30)$ degrees. The largest angle is:

The angles of a quadrilateral are $(x), (x+10), (x+20)$ and $(x+30)$ degrees. The largest angle is:
  1. $75^{\circ}$
  2. $95^{\circ}$
  3. $105^{\circ}$
  4. $120^{\circ}$

Solution

Sum $= 4x + 60 = 360 \Rightarrow x = 75$. Largest angle $= x + 30 = 105^{\circ}$.

Asked in: IMO

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