Two adjacent angles of a parallelogram are in the ratio $2:3$. The smaller angle is:

Two adjacent angles of a parallelogram are in the ratio $2:3$. The smaller angle is:
  1. $60^{\circ}$
  2. $72^{\circ}$
  3. $80^{\circ}$
  4. $108^{\circ}$

Solution

Adjacent angles are supplementary: $2x + 3x = 180 \Rightarrow x = 36$. Smaller angle $= 2x = 72^{\circ}$.

Asked in: IMO

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