Which polygon is a convex heptagon? A polygon has 7 sides. No angles go inside of the shape. A polygon has 8 sides. No angles go inside of the shape. A polygon has 8 sides. One angle goes inside of the shape. A polygon has 7 sides. One angle goes inside of the shape. please it’s for a unit test
The correct answer and explanation is:
The correct answer is: A polygon has 7 sides. No angles go inside of the shape.
A convex heptagon is a polygon that has seven sides and, importantly, no angles pointing inward. This means that all of its interior angles are less than 180 degrees, and all vertices point outward, forming a convex shape.
To understand why this is the correct description of a convex heptagon, let’s first break down the characteristics of polygons:
- A heptagon is a polygon with seven sides. When you look at its exterior, it has seven straight edges that form a closed shape.
- A convex polygon is one in which all of the interior angles are less than 180 degrees. This ensures that no angle of the polygon points inward or creates a concave shape, which would have one or more interior angles greater than 180 degrees.
For a polygon to be classified as convex, all of its angles must lie on the outside of the shape. If even one of the interior angles is greater than 180 degrees, it would be considered concave, and it would not be a convex polygon. Therefore, in the case of the convex heptagon, all of its seven sides are arranged in a way that no interior angle points inward.
Now, let’s review the other choices to clarify:
- A polygon has 8 sides. No angles go inside of the shape. This is a convex octagon, not a heptagon. It has eight sides and no inward angles.
- A polygon has 8 sides. One angle goes inside of the shape. This is a concave octagon. The inward angle means at least one of the angles is greater than 180 degrees.
- A polygon has 7 sides. One angle goes inside of the shape. This is a concave heptagon. The inward angle makes it not convex.
Thus, the first description correctly identifies a convex heptagon.