In quadrilateral $ABCD$, the angles are in the ratio $3:5:9:13$. The largest angle is:

In quadrilateral $ABCD$, the angles are in the ratio $3:5:9:13$. The largest angle is:
  1. $108^{\circ}$
  2. $117^{\circ}$
  3. $144^{\circ}$
  4. $156^{\circ}$

Solution

$3x + 5x + 9x + 13x = 30x = 360 \Rightarrow x = 12^{\circ}$. Largest $= 13x = 156^{\circ}$.

Asked in: IMO

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