Question 694162
In a triangle the sum of angles is {{{A+B+C=180}}} degrees.

 
 if angle {{{A}}} is {{{60}}} percent of angle {{{C}}},than

{{{A=(60/100)C}}}.....=>...{{{A=0.60C}}}


 and if angle {{{B}}} is {{{150}}} percent of angle {{{A}}}, than 

{{{B=(150/100)A}}}....=>...{{{B=1.5(0.60C)}}}=>...{{{B=0.9C)}}}

so, plug it in  {{{A+B+C=180}}}

 {{{0.60C+0.9C+C=180}}}.....solve for {{{C}}}

{{{2.5C=180}}}

{{{C=180/2.5}}}

{{{highlight(C=72)}}}

=>...{{{A=0.60C}}}

{{{A=0.60*72}}}

{{{highlight(A=43.2)}}}

=>...{{{B=0.9C)}}}

{{{B=0.9C)}}}

{{{B=0.9*72)}}}

{{{highlight(B=64.8))}}}

so, the smallest angle of the triangle measure {{{highlight(43.2)}}}