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Question 482704: The largest angle in a triangle is 55 degrees more than the smallest angle. The sum of the measures of the two smaller angles is 10 degrees more than the measure of the largest angle. Let x,y,z be the measures of the three angles from largest to smallest. write a system of three linear equations whose solution gives the meausres of each angle
Answer by cleomenius(959)   (Show Source):
You can put this solution on YOUR website! x = largest angle
y = middle angle
z = smallest angle
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I set the 3 equations up as follows:
x = z + 55
x = y + z -10
x + y + z = 180
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x -z = 55
x - y -z = -10
x + y + z = 65
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multiply the first equation by -1
-x + z = -55
and add to equation 2.
-y = -65
therefore y = 65.
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Now plug in 65 to equation 3 for y.
x + z = 115
Add equation 1 to 3.
2x = 170
x = 85
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180 - 85 + 65 = 30, the value for z
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To check, 85 = 30 + 55
65 + 30 = 95 - 10.
Cleomenius.
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