Question

Divide the circle into, 3, 4, 5, 6, 8, 9, 10, 12 equal parts complete the regular polygons mark the measure of polygons

Answer 1

The division of a circle into, 3, 4, 5, 6, 8, 9, 10, 12 equal parts and the completion of the regular polygons and their measures is done as follows:

• When a circle is divided into 3 equal parts, a triangle is obtained.  
• The sum of angles in a triangle is 180°.
• When a circle is divided into 4 equal parts, a quadrilateral is obtained.  
• The sum of angles in a quadrilateral is 360°.
• When a circle is divided into 5 equal parts, a pentagon is obtained.  
• The sum of angles in a pentagon is 540°.
• When a circle is divided into 6 equal parts, a hexagon is obtained.  
• The sum of angles in a hexagon is 720°.
• When a circle is divided into 8 equal parts, an octagon is obtained.  
• The sum of angles in an octagon is 1080°.
• When a circle is divided into 9 equal parts, a nonagon is obtained.  
• The sum of angles in a nanogon is 1260°.
• When a circle is divided into 10 equal parts, a decagon is obtained.  
• The sum of angles in a decagon is 1440°.
• When a circle is divided into 12 equal parts, a dodecagon is obtained.
• The sum of angles in a dodecagon is 1800°.