geometry: Prove angle A does not equal 60°

[icec]

geometry: Prove angle A does not equal 60°

Please help with this problem:

Given: In triangle ABC, the measure of angle B is 120 degrees.
Prove: The measure of angle A does not equal 60 degrees.
Plan: Use an indirect proof.

 

[pka]

Each measure must be positive: \(\displaystyle m\angle K > 0,\quad K = A,B,C\).

Moreover, \(\displaystyle m\angle A + m\angle B + m\angle C = 180^o\) must also be true.

Use the given to show you get a contradiction if \(\displaystyle m\angle A = 60^0\).