Sum of Interior Angles

The sum of all but one of the interior angles of a convex polygon equals 2570°. The remaining angle is:

  1. 90°
  2. 105°
  3. 120°
  4. 130°
  5. 144°


Show/Hide Solution

The sum of the interior angles of an n-gon is (n – 2)180°. We see that:

2570° = 14(180°) + 50° = 15(180°) – 130°.

Therefore, the missing angle in the 17-gon must be 130°. The answer is (d).

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