Grades 11-12 Video Solutions 2013-Levels 11&12 Video Solutions 2013 problem18

Levels 11&12 Video Solutions 2013 problem18

Video Transcription

Video Summary

In triangle ABC, points M and N on side AB create two isosceles triangles: one where AN = AC and another where BM = BC. The task is to find angle ACB, knowing angle MCN is 43 degrees. The solution involves setting up equations for the angles in these isosceles triangles and finding the supplementary relationships. By solving these equations, the individual angle sum alpha + beta is determined to be 51 degrees. Adding this to the given 43 degrees, the vertex angle ACB is found to be 94 degrees. The final answer is E.

Keywords

triangle geometry

isosceles triangles

angle calculation

supplementary angles

vertex angle