Question 111468


Given:   In triangle ABC, angle {{{B = 120^ o}}}

Proven:  angel A {{{A}}} is not equal to {{{60^ o}}}  


If you use an indirect proof, you need to assume what you need {{{to}}}{{{ prove}}}{{{ is}}}{{{ false}}}, and then show that something contradictory (absurd) happens.

You will need following steps:

Assume that the {{{opposite}}} of what you are trying to prove is true; in 

other words, assume that angle is {{{A=60^ o}}}
 
as we know, {{{the}}}{{{ sum}}}{{{ of}}}{{{ all}}}{{{ three}}}{{{ angles}}} of 
a triangle is equal to {{{180^ o }}}degrees.

{{{A + B + C = 180^ o}}}

you can solve for {{{C}}} 

{{{ C = 180^ o - (A + B)}}}

{{{ C = 180^ o - (60^ o+ 120^ o)}}}

{{{ C = 180^ o -  180^ o}}}

{{{ C = 0 }}}.....it is {{{absurd}}} to have one of three angles in a 
triangle equal to {{{0}}}


So, you can conclude that, as it was proven, angel {{{A}}} is not equal to {{{60^ o}}}