In parallelogram $ABCD$, $\angle A : \angle B = 4:5$. Then $\angle A$ equals:

In parallelogram $ABCD$, $\angle A : \angle B = 4:5$. Then $\angle A$ equals:
  1. $72^{\circ}$
  2. $80^{\circ}$
  3. $100^{\circ}$
  4. $108^{\circ}$

Solution

$\angle A$ and $\angle B$ are adjacent, so $4x + 5x = 180 \Rightarrow x = 20$. $\angle A = 4 \cdot 20 = 80^{\circ}$.

Asked in: IMO

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