Question

question 3

1. a polygon is

many triangles
a flat figure (no depth)
any closed shape with straight sides.
any 2d figure
how does the number of sides of a convex polygon, n, relate to the sum of measures of its interior angles?
you know that the sum of the interior angle measures of a triangle is 180°. decompose polygons into triangles and look for a pattern.
to decompose a convex polygon into triangles, construct all diagonals from one vertex.

Explanation:

A polygon is defined as a closed shape with straight sides. Let's analyze the options:

• "Many Triangles": Incorrect, a polygon isn't defined as many triangles (though it can be decomposed into them).
• "A flat figure (no depth)": This describes a 2D figure in general, not specifically a polygon (e.g., a circle is flat but not a polygon).
• "Any closed shape with straight sides": Correct, as polygons are closed, 2D shapes with straight edges (sides).
• "Any 2D figure": Incorrect, as 2D figures like circles don't have straight sides and aren't polygons.

Answer:

The correct option is the one labeled "Any closed shape with straight sides." (Assuming the option with this text is, for example, the second option from the left in the provided choices, but based on the description, the answer is the option stating "Any closed shape with straight sides.")