Question 631521


the sum of the measures of two obtuse angles is 215,the sum of 3/5 of the supplement of the smaller angle and 2/3 the supplement of larger angle is 91. find the measure of the angles.


Let larger angle be L, and smaller S
Then: L + S = 215 ---- L = 215 – S ------ eq (i)
Supplement of the larger angle = 180 – L
Supplement of the smaller angle = 180 – S


{{{3/5*(180 - S) + 2/3*(180 - L) = 91}}} ---- {{{(540 - 3S)/5 + (360 - 2L)/3 = 91}}}


3(540 – 3S) + 5(360 – 2L) = 1,365 ------ Multiplying by LCD, 15
1,620 – 9S + 1,800 – 10L = 1,365 
– 10L – 9S = - 2,055 ------ eq (ii) 


- 10(215 – S) – 9S = - 2,055 ------- Substituting 215 – S for L in eq (ii) 
– 2,150 + 10S – 9S = - 2,055 
S = - 2,055 + 2,150 
S, or smaller angle = {{{highlight_green(95)}}}


L = 215 – 95 ------ Substituting 95 for S in eq (i)


L, or larger angle = {{{highlight_green(120)}}}


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