Question

Match the number of triangles formed or the interior angle sum to each regular polygon.

(LOOK AT THE PICTURE FOR IT TO MAKE SENSE)

number of triangles
formed Is 4

Interior angle sum
Is 1,440

Interior angle sum
Is 1,800

number of triangles
formed Is 6

regular
octagon
0
O
regular hexagon regular decagon regular dodecagon
0
O
0
D

Answer 1

Number of triangles formed is 4:

octagon (?)

Interior angle sum is 1440°:

to find the number of sides (and thus the geometric figure) from the sum of the interior angles, use the formula:

(interior angle sum)÷180 = N-2

1440÷180 = N-2

N = 10

so the figure is decagon

Interior angle sum is 1800°:

1800÷180 = N-2

N = 12

so it's dodecagon

Number of triangles formed is 6:

hexagon

Answer 2

Sum of the interior angles = (number of sides in a polygon - 2) * 180

1. Number of triangles formed is 4: Hexagon

Draw all the diagonals of a regular hexagon. You will notice that it divides the hexagon into six congruent triangles. So, you can form 4 triangles by selecting any 4 vertices of the hexagon, and connecting them to form a quadrilateral, which can then be divided into 2 triangles.

For a regular decagon, dodecagon, or octagon, it is not possible to form 4 triangles by selecting only 4 vertices of the polygon, since the minimum number of diagonals needed to divide the polygon into 4 triangles is 5 for a decagon, 6 for a dodecagon, and 7 for an octagon.

2. Interior angle sum is 1,440 degrees: Decagon (has 10 sides)

Sum of the interior angles = (number of sides in a polygon - 2) * 180

Sum = (10-2) * 180

Sum = 8 * 180

Sum = 1,440 degrees

3. Interior angle sum is 1,800 degrees: Dodecagon (has 12 sides)

Sum of the interior angles = (number of sides in a polygon - 2) * 180

Sum = (12-2) * 180

Sum = 10 * 180

Sum = 1,800 degrees

4. Number of triangles formed is 6: Hexagon & Octagon

A regular hexagon is a six-sided polygon where all six sides are equal in length, and all six interior angles are equal to 120 degrees. To form six triangles from a regular hexagon, we need to draw all the diagonals of the hexagon.

A diagonal is a line segment that connects two non-adjacent vertices of the hexagon. In a regular hexagon, there are three types of diagonals:

• Short diagonals: These diagonals connect two vertices that are adjacent to each other. There are six short diagonals in a regular hexagon.
• Medium diagonals: These diagonals connect two vertices that are not adjacent to each other, but that are separated by one vertex. There are six medium diagonals in a regular hexagon.
• Long diagonals: These diagonals connect two vertices that are not adjacent to each other, and that are separated by two vertices. There are two long diagonals in a regular hexagon.

When we draw all the diagonals of a regular hexagon, we divide the hexagon into six congruent triangles, each with a central angle of 120 degrees. Each vertex of the hexagon is connected to two other vertices by a diagonal, which divides the hexagon into two congruent triangles. Since there are six vertices in a regular hexagon, we get a total of six triangles when we draw all the diagonals.

And the same logic applies for octagons

Hope this helps