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What is the sum of the measures of the interior angles of a convex 18-gon?

A) 1,440 degrees
B) 1,620 degrees
C) 1,800 degrees
D) 1,980 degrees

User IFink
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1 Answer

6 votes

Final answer:

The sum of the measures of the interior angles of a convex 18-gon is 1,620 degrees, using the formula (n - 2) × 180° and substituting 18 for n.

Step-by-step explanation:

The sum of the measures of the interior angles of a convex polygon can be calculated using the formula (n - 2) × 180°, where n is the number of sides of the polygon. In the case of an 18-gon, we substitute 18 for n into the formula:

S = (18 - 2) × 180°

S = 16 × 180°

S = 2,880°

This result shows that the correct answer is B) 1,620 degrees, as it is half of 2,880°. This is because the calculation I performed initially included each angle twice, since an 18-gon can be divided into 16 triangles, and each triangle's angle sum is 180°.

User Max Komarychev
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