## How do you construct a pentagon in geometry?

In geometry, a pentagon (from the Greek πέντε pente meaning five and γωνία gonia meaning angle) is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°….

Pentagon | |
---|---|

Edges and vertices | 5 |

Internal angle (degrees) | 108° (if equiangular, including regular) |

### What is each angle of a pentagon?

108 degrees

There are 5 interior angles in a pentagon. Divide the total possible angle by 5 to determine the value of one interior angle. Each interior angle of a pentagon is 108 degrees.

#### How do you draw a pentagon pentagon?

How to Draw a Perfect Pentagon

- The first step to draw a perfect pentagon is to mark a dot in the center of your paper.
- Using the central dot and a protractor, divide the circle into 5 points.
- Connect every adjacent point.
- You can also draw a pentagon with a compass and a ruler if a circle is given.

**How do you construct a pentagon of a triangle?**

If we divide a pentagon into triangles as in the figure on the left below, the pentagon is made up of 3 triangles, so the angle sum is 180 + 180 + 180 = 3*180 = 540 degrees. However, the non-convex pentagon on the right is a trickier case….Angles in Isosceles Triangles.

a | b |
---|---|

90 | |

60 | |

36 | |

72 |

**How do you make a perfect pentagon with a compass?**

Put the point of the compass on M and extend it so the pencil touches A. Draw an arc that crosses line XO; we will call this intersection “R”. Move the point of the compass onto A and extend it so the pencil now touches R. The radius of your compass is now equal to the length of the sides of your pentagram.

## How do you make a pentagon on graph paper?

Place the point of the compass on “C.” Move the arm so the tip of the pencil touches “A.” Draw a circle. Follow the horizontal line left until it intersects with the new circle. Mark that point with a “D.” Place the point of the compass on “A.” Move the arm so the tip of the pencil touches “D.” Draw a circle.