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. squares, octagons
● b. squares, heptagon
● c. squares, triangles

b. the number of angles is □
choose the correct answer below
● a. 60°, 60°, 90°, 120°
● b. 60°, 60°, 60°, 90°, 90°
● c. 60°, 60°, 60°, 60°, 120°

c. choose the correct answer below
● the tessellation is possible because the sum of measures of all angles that come together at the vertex is less than 360°
● the tessellation is possible because the sum of measures of all angles that come together at the vertex is 360°

Explanation:

Part (a)

Step 1: Analyze the tessellation

Looking at the given tessellation, we can see two types of regular polygons: squares (with 4 sides, right angles) and triangles (with 3 sides, 60° angles). The other options (A: octagons, B: heptagon) don't match the shapes in the figure.

Step 1: Count the angles at a vertex

By examining the vertex where the polygons meet, we can see that there are 5 angles coming together. Let's check the angle measures: triangles have 60° angles and squares have 90° angles. Looking at the options, option B has angles \(60^\circ, 60^\circ, 60^\circ, 90^\circ, 90^\circ\). Let's sum them: \(60 + 60 + 60 + 90 + 90 = 360^\circ\), which makes sense for a tessellation (angles around a point sum to 360°). The number of angles is 5.

Step 1: Recall tessellation condition

For a tessellation to be possible, the sum of the measures of all angles that come together at a vertex must be \(360^\circ\) (since a full circle around a point is \(360^\circ\)). The first option says the sum is less than \(360^\circ\), which is incorrect. The second option states the sum is \(360^\circ\), which is the correct condition.

Answer:

C. squares, triangles

Part (b)