Four angles of a pentagon are $110^{\circ}, 100^{\circ}, 95^{\circ}$ and $130^{\circ}$. The fifth angle is:

Four angles of a pentagon are $110^{\circ}, 100^{\circ}, 95^{\circ}$ and $130^{\circ}$. The fifth angle is:
  1. $95^{\circ}$
  2. $100^{\circ}$
  3. $105^{\circ}$
  4. $115^{\circ}$

Solution

Sum of interior angles of a pentagon $= 540^{\circ}$. Fifth angle $= 540 - (110+100+95+130) = 540 - 435 = 105^{\circ}$.

Asked in: IMO

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