3310.11 – Sum of Interior Angles

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

  1. 90∘^{\circ}
  2. 105∘^{\circ}
  3. 120∘^{\circ}
  4. 130∘^{\circ}
  5. 144∘^{\circ}
Solution

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

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

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