SOLUTION: 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 angl

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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.
Answer by MathTherapy(10557) About Me  (Show Source):
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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%2F5%2A%28180+-+S%29+%2B+2%2F3%2A%28180+-+L%29+=+91 ---- %28540+-+3S%29%2F5+%2B+%28360+-+2L%29%2F3+=+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%2895%29

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

L, or larger angle = highlight_green%28120%29

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