Use the image to answer the question.

Question

An illustration shows two square construction signs. Starting with the vertex on the left, the vertices are labeled A, B, C, and D. The sign on the left is labeled figure 1, and the sign on the right is labeled figure 2. In figure 1, lines connect the vertices A and C and B and D. In figure 2, a line connects the vertices B and D. An image on both signs shows a silhouette of a person holding a shovel.

Choose the correct decomposition of the polygon into n−2 triangles.
(1 point)
Responses

Figure 1 is the correct decomposition because Figure 1 is decomposed into 2 triangles that are equal sizes.
Figure 1 is the correct decomposition because Figure 1 is decomposed into 2 triangles that are equal sizes.
Figure 1 is the correct decomposition because it has 4 triangles of the equal size.
Figure 1 is the correct decomposition because it has 4 triangles of the equal size.
Figure 2 is the correct decomposition because it has n−2=4−2=2 triangles.
Figure 2 is the correct decomposition because it has n minus 2 equals 4 minus 2 equals 2 triangles.
Figure 1 is the correct decomposition because Figure 1 is decomposed into 4 triangles that are not equal sizes.

Answer 1

Figure 1 is the correct decomposition because Figure 1 is decomposed into 4 triangles that are not equal sizes.

Answer 2

Use the image to answer the question.

An illustration shows a bee on top of a square honeycomb. The cells inside the honeycomb are shaped like hexagons. In one of the cells, lines connect the vertex at the top left to the three non-adjacent vertices.

Is this the correct decomposition of a honeycomb shaped like a hexagon into n−2 triangles?
(1 point)
Responses

Yes, this is the correct decomposition because the decomposition has n−2=6−2=4 triangles.
Yes, this is the correct decomposition because the decomposition has n minus 2 equals 6 minus 2 equals 4 triangles.
Yes, this is the correct decomposition because the decomposition is 6 triangles.
Yes, this is the correct decomposition because the decomposition is 6 triangles.
No, this is not the correct decomposition because the decomposition is 4 equal-sized triangles.
No, this is not the correct decomposition because the decomposition is 4 equal-sized triangles.
No, this is not the correct decomposition because the decomposition is 4 triangles.

Answer 3

No, this is not the correct decomposition because the decomposition is 4 triangles.

Answer 4

Use the angle sum of triangles to develop the interior angle sums of regular polygons formula using decomposition. Test the formula by finding the sum of the interior angles of a square.(1 point)
Responses

The sum of the angles of a square is 182°.
The sum of the angles of a square is 182 degrees .
The sum of the angles of a square is 360°.
The sum of the angles of a square is 360 degrees .
The sum of the angles of a square is 1,080°.
The sum of the angles of a square is 1,080 degrees .
The sum of the angles of a square is 1,440°.
The sum of the angles of a square is 1,440 degrees .

Answer 5

The sum of the angles of a square is 360 degrees.

Answer 6

When a regular polygon with n sides is decomposed into triangles using the same vertex, how many triangles are formed?(1 point)
Responses

When a regular polygon is decomposed, 2⋅n triangles are formed, where n is the number of sides of the regular polygon. There are twice as many triangles formed than the number of the sides of the regular polygon.
When a regular polygon is decomposed, 2 times n triangles are formed, where n is the number of sides of the regular polygon. There are twice as many triangles formed than the number of the sides of the regular polygon.
When a regular polygon is decomposed, n triangles are formed, where n is the number of sides of the regular polygon.
When a regular polygon is decomposed, n triangles are formed, where n is the number of sides of the regular polygon.
When a regular polygon is decomposed, n−2 triangles are formed, where n is the number of sides of the regular polygon. There are two fewer triangles than the number of the sides of the regular polygon.
When a regular polygon is decomposed, n minus 2 triangles are formed, where n is the number of sides of the regular polygon. There are two fewer triangles than the number of the sides of the regular polygon.
When a regular polygon is decomposed, n+2 triangles are formed, where n is the number of sides of the regular polygon. There are two more triangles than the number of the sides of the regular polygon.
When a regular polygon is decomposed, n plus 2 triangles are formed, where n is the number of sides of the regular polygon. There are two more triangles than the number of the sides of the regular polygon.

Answer 7

When a regular polygon is decomposed, n-2 triangles are formed, where n is the number of sides of the regular polygon. There are two fewer triangles than the number of the sides of the regular polygon.

Answer 8

Why was Stephen Austin able to establish a colony in Mexican territory?
(1 point)
Responses

The Mexican government gave him a land grant.
The Mexican government gave him a land grant.
He claimed the land for himself.
He claimed the land for himself.
The U.S. government gave him an exemption.
The U.S. government gave him an exemption.
The local farmers were generous.

Answer 9

The Mexican government gave him a land grant.