In a pie chart, $4$ items have angles $90^{\circ}, 120^{\circ}, 60^{\circ}, x^{\circ}$. Find $x$.

In a pie chart, $4$ items have angles $90^{\circ}, 120^{\circ}, 60^{\circ}, x^{\circ}$. Find $x$.
  1. $60^{\circ}$
  2. $80^{\circ}$
  3. $90^{\circ}$
  4. $120^{\circ}$

Solution

Sum $= 360^{\circ} \Rightarrow x = 360 - (90+120+60) = 360-270 = 90^{\circ}$.

Asked in: IMO

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