The angles of a pentagon are $x^{\circ}, (x+20)^{\circ}, (x+40)^{\circ}, (x+60)^{\circ}$ and…

The angles of a pentagon are $x^{\circ}, (x+20)^{\circ}, (x+40)^{\circ}, (x+60)^{\circ}$ and $(x+80)^{\circ}$. The smallest angle is:
  1. $58^{\circ}$
  2. $68^{\circ}$
  3. $78^{\circ}$
  4. $108^{\circ}$

Solution

Sum $= 5x + 200 = 540 \Rightarrow 5x = 340 \Rightarrow x = 68^{\circ}$. Smallest angle $= x = 68^{\circ}$.

Asked in: IMO

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