Geometry

Question Analysis

The main focus of this question is to determine whether the given shape meets the criteria of a regular polygon. It tests the understanding of the key properties that define regular polygons.

 

Key Concept Explanation

Regular Polygons: A regular polygon must be both equilateral (all sides have equal length) and equiangular (all interior angles have equal measure).

 

Step - by - Step Solution

1. Examine the side lengths: The side lengths of the polygon are 46, 58, 63, and 49. Since these side lengths are not all equal, the polygon is not equilateral.

2. Examine the angle measures: The angle measures are 98°, 112°, 87°, and 63°. Since these angle measures are not all equal, the polygon is not equiangular.

 

Since the shape fails to be both equilateral and equiangular, it does not meet the definition of a regular polygon.

 

Option Analysis

Yes: This option is incorrect. The shape is neither equilateral nor equiangular, so it cannot be a regular polygon.

No: This is the correct option. The polygon does not satisfy the requirements of being both equilateral and equiangular.

 

Common Mistakes

Assuming that a polygon is regular if it ...