MATH SOLVE

5 months ago

Q:
# Which of the following statements are correct? Select all that apply.1. The regular polygon ABCDEFG is made up of 7 equilateral triangles 2. The regular polygon ABCDEFG has 14 diagonals 3. The regular polygon ABCDEFG can be broken down into 2 isosceles trapezoids and 1 isosceles triangle 4. The apothem of the regular polygon ABCDEFG is greater than the radius 5. The central angle of the polygon ABCDEFG is about 51.43° and each interior angle is about 128.57°6. The area of the circumcircle will be the same as the area of the polygon.7. The central angle ABCDEFG is the same measure of the exterior angle

Accepted Solution

A:

For a 7 sides polygon which is called heptagon or septagon

Interior angles = (7-2)*180/7 = 128.57°

Exterior angle = 180 - 128.57 = 51.43°

Central angle = 360/7 = 51.43°

The statements which are correct:

3. The regular polygon ABCDEFG can be broken down into 2 isosceles trapezoids and 1 isosceles triangle

5. The central angle of the polygon ABCDEFG is about 51.43° and each interior angle is about 128.57°

7. The central angle ABCDEFG is the same measure of the exterior angle

Interior angles = (7-2)*180/7 = 128.57°

Exterior angle = 180 - 128.57 = 51.43°

Central angle = 360/7 = 51.43°

The statements which are correct:

3. The regular polygon ABCDEFG can be broken down into 2 isosceles trapezoids and 1 isosceles triangle

5. The central angle of the polygon ABCDEFG is about 51.43° and each interior angle is about 128.57°

7. The central angle ABCDEFG is the same measure of the exterior angle