Question 1194130


The sum of the measures of an acute angle and an obtuse angle is {{{140}}}. 
let an acute angle be {{{x}}} and an obtuse angle {{{y}}}

{{{x + y = 140}}}

{{{x = 140-y}}}.........eq.1

The sum of twice the supplement of the obtuse angle and three times the complement of the acute angle is {{{340}}}. 

if
the supplement of the obtuse angle: {{{180 - x}}}
 the complement of the acute angle:{{{90 - x}}}

we have:

{{{2(180 - x) + 3(90 - y) = 340}}}

since {{{x = 140 - y}}}

{{{2(180 - (140 - y)) + 3(90 - y) = 340}}}

{{{2(180 - 140 + y) + 3(90 - y) = 340}}}

{{{2(40 + y) + 3(90 - y) = 340}}}

{{{80 + 2y + 270 - 3y= 340}}}

{{{350  - y= 340}}}

{{{y = 350-340}}}

{{{y = 10}}}

{{{x = 140-10}}}

{{{x = 130}}}

 the measures of the angles are: {{{ 10}}} and {{{ 130}}}