3310.11 – Sum of Interior Angles

The sum of all but one of the interior angles of a convex polygon equals 2570∘2570^{\circ}. What's the remaining angle?

  1. 90∘90^{\circ}

  2. 105∘105^{\circ}

  3. 120∘120^{\circ}

  4. 130∘130^{\circ}

  5. 144∘144^{\circ}

Solution

The sum of the interior angles of an nn-gon is (n−2)180∘(n - 2)180^{\circ}.

We see that 2570∘=14(180∘)+50∘=15(180∘)−130∘2570^\circ = 14(180^\circ) + 50^\circ = 15(180^\circ) - 130^\circ.

Therefore, the missing angle in the 17-gon must be 130∘130^\circ. The answer is d.