The interior angles of a quadrilateral are in the ratio $1:2:3:4$. The smallest angle is:

The interior angles of a quadrilateral are in the ratio $1:2:3:4$. The smallest angle is:
  1. $30^{\circ}$
  2. $36^{\circ}$
  3. $40^{\circ}$
  4. $45^{\circ}$

Solution

Sum $= 360^{\circ}$. $1x+2x+3x+4x = 10x = 360 \Rightarrow x = 36^{\circ}$. Smallest angle $= x = 36^{\circ}$.

Asked in: IMO

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