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A hectogon has 100 sides. Draw in the diagonals, (Just kidding - Ain't nobody got time for that!)1. How many triangles would you be able to create? (from one vertex)2. What is the sum of the interior angles in each triangle?2. What is the sum of the interior angles in the hectogon?

Question

A hectogon has 100 sides. Draw in the diagonals, (Just kidding - Ain't nobody got time for that!)1. How many triangles would you be able to create? (from one vertex)2. What is the sum of the interior angles in each triangle?2. What is the sum of the interior angles in the hectogon?

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Solution

  1. A hectogon has 100 sides. If you draw lines from one vertex to all other non-adjacent vertices, you can create triangles. Since the two adjacent vertices cannot be used to form a triangle, you subtract 2 from the total number of sides. So, you can create 100 - 2 = 98 triangles from one vertex.

  2. The sum of the interior angles in each triangle is always 180 degrees, regardless of the shape of the triangle.

  3. The sum of the interior angles in a polygon can be calculated using the formula (n-2) * 180, where n is the number of sides. So, for a hectogon, the sum of the interior angles would be (100-2) * 180 = 17640 degrees.

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