In parallelogram $ABCD$, $\angle A = (3x - 10)^{\circ}$ and $\angle C = (x + 50)^{\circ}$. Then $x$ equals:

In parallelogram $ABCD$, $\angle A = (3x - 10)^{\circ}$ and $\angle C = (x + 50)^{\circ}$. Then $x$ equals:
  1. $20$
  2. $25$
  3. $30$
  4. $35$

Solution

Opposite angles of a parallelogram are equal: $3x - 10 = x + 50 \Rightarrow 2x = 60 \Rightarrow x = 30$.

Asked in: IMO

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