Question

the given tessellation formed by two or more regular polygons is shown. a. name the type of regular polygons that surround each vertex. b. determine the number of angles that come together at each vertex, as well as the measures of these angles. c. use the angle measures from part (b) to explain why the tessellation is possible. a. choose the correct answer below. a. triangle, pentagons b. triangles, hexagons c. triangle, squares b. the number of angles is

Explanation:

Step1: Identify polygon types

The tessellation contains triangles and squares.

Step2: Recall angle - sum property at a vertex

For a tessellation to be possible, the sum of the angles at each vertex must be 360°. The interior angle of a square is 90° and the interior angle of an equilateral triangle is 60°.

Step3: Analyze angles at a vertex

At each vertex, we can see combinations of these angles that add up to 360°. For example, we can have 2 squares (2×90° = 180°) and 3 triangles (3×60°=180°), 180° + 180°=360°.

Answer:

a. Triangle, squares
b. At each vertex, the number of angles and their measures combine to 360°. For instance, 2 squares (each with 90° angle) and 3 triangles (each with 60° angle) sum to 2×90°+3×60° = 180°+180° = 360°.
c. Since the sum of the angles of the regular polygons (squares and triangles) that meet at each vertex is 360°, the tessellation is possible.