Question 119671


If the angles in triangle {{{ABC}}} are {{{A}}},{{{B}}}, and {{{C}}}, then:

the angle {{{A = 5x}}}

the angle {{{B = 4x-1 }}} and 

the angle {{{C = 3x+13}}}

Since their sum is {{{ 180}}}, we will have:

{{{A + B + C = 180}}}……….substitute {{{A}}},{{{B}}}, and {{{C}}}

{{{5x + (4x-1 ) + (3x+13) = 180}}}……….solve for {{{x}}}

{{{5x + 4x -1 + 3x +13 = 180}}}……….

{{{12x  +12 = 180}}}……….

{{{12x  = 180 - 12}}}……….

{{{12x  = 168}}}……….

{{{x  = 168/12}}}……….

{{{x  = 14}}}……….

Now calculate each angle:

{{{A = 5x}}}……………… substitute {{{x }}}……….

{{{A = 5*14}}}

{{{A = 70}}}………… the angle{{{A }}}



{{{B = 4*14 - 1 }}}………….. substitute {{{x }}}……….

{{{B = 56 - 1 }}}

{{{B = 55}}}…………….. the angle{{{B }}}

{{{C = 3*14 +13}}}……………… substitute {{{x }}}……….

{{{C = 42 +13}}}

{{{C = 55}}}…………. the angle{{{C }}}


Check their sum:

{{{A + B + C = 180}}}……….

{{{70 + 55 + 55 = 180}}}……….

{{{70 + 110 = 180}}}……….

{{{180 = 180}}}……….