Which type of polygon has at least one angle greater than 180 degrees?

Which type of polygon has at least one angle greater than 180 degrees?

• A. Convex Polygon
• B. Concave Polygon
• C. Regular Polygon
• D. Simple Polygon

Answer: (B)

The correct choice identifies a concave polygon as one that contains at least one interior angle greater than 180 degrees. In a concave polygon, the shape "caves inward," which creates this larger angle. This geometry is crucial for defining concave shapes because the presence of an angle exceeding 180 degrees indicates that at least one vertex points inward relative to the shape’s overall outline. In contrast, a convex polygon features all interior angles measuring less than 180 degrees, ensuring that no vertex points inward. Regular polygons, which fall under the category of convex polygons, have equal sides and angles; thus, they cannot have any angles greater than 180 degrees. Simple polygons are those that do not intersect themselves, which can include both concave and convex shapes, but they do not specifically address the situation of angles exceeding 180 degrees like concave polygons do. Therefore, distinguishing concave polygons helps recognize the unique characteristic of having one or more angles greater than 180 degrees.

The correct choice identifies a concave polygon as one that contains at least one interior angle greater than 180 degrees. In a concave polygon, the shape "caves inward," which creates this larger angle. This geometry is crucial for defining concave shapes because the presence of an angle exceeding 180 degrees indicates that at least one vertex points inward relative to the shape’s overall outline.

In contrast, a convex polygon features all interior angles measuring less than 180 degrees, ensuring that no vertex points inward. Regular polygons, which fall under the category of convex polygons, have equal sides and angles; thus, they cannot have any angles greater than 180 degrees. Simple polygons are those that do not intersect themselves, which can include both concave and convex shapes, but they do not specifically address the situation of angles exceeding 180 degrees like concave polygons do. Therefore, distinguishing concave polygons helps recognize the unique characteristic of having one or more angles greater than 180 degrees.