Grades 11-12 Video Solutions 2013-Levels 11&12 Video Solutions 2013 problem11

Levels 11&12 Video Solutions 2013 problem11

Video Transcription

Video Summary

Radu uses identical regular pentagon pieces to form a circle by gluing them edge to edge. To determine the number of pentagons needed, the method involves finding the central angle (alpha) formed by extending the edges to the circle's center. Each pentagon's central angle is 72 degrees, leading to an interior angle of 108 degrees. The supplemental angle beta thus measures 72 degrees. Therefore, alpha, as part of an isosceles triangle with beta, measures 36 degrees. Dividing 360 degrees by 36 gives 10, indicating that 10 pentagons are required to complete the circle.

Keywords

regular pentagon

central angle

isosceles triangle

circle formation

geometry