how to draw a 72 deg. sector in a given circle of radius 3.7 cm.?

Question

Draw 72 deg sector of circle by using compass pencil & scale only.

Answer 1

The circle radius (r) = 3.7 cm ,

Circle sector is also known as a "pie piece", the portion of a circle enclosed by two radii and an arc.

There are several interesting ways to construct a sector.

In this case to draw the 72 degrees sector we use  with the help of regular pentagon.

To draw the 72  degrees sector

Draw a circleof radius 3.7 cm center at the origin.

The angle at the center of a regular pentagon is 360/5 = 72degrees.

Hence the distance between the five vertices is the same as the radius of the circumcircle.

Choose the vertices are A, B , C , D , E.

Choose a distance r. Draw a circle of radius r. Choose any point on the circle and mark points
distance r apart using compasses. Then join up the pentagon.

A second construction would be to draw five equilateral triangles, as shown in the diagram.

From the diagram we observe  five sectors AOB , AOE, BOC , COD , DOE.

And each sector angle is 72 degrees.