Question 49567: The measure of one angle of a triangle is 30 degrees less than the measute of the second angle. The measure of the third angle is 20 degrees less than the sum of the measures of the other two. find the measures of each angle of the triangle.
sorry, I have been trying to solve this but I can't
-mc
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let the first angle be A.
The second angle be B.
The third angle be C.
Recall that in any triangle, the sum of the angles = 180 degreea.
A+B+C = 180
From the problem desciption, you get:
A = B-30 The measure of one angle is 30 degrees less than the second angle.
C = (A+B)-20 The third angle is 20 degrees less than the sum of the other two. Substituting (A=B-30) from above, you can rewrite this as:
C = (B-30)+B-20. Simplify.
C = 2B-50 Now substitute A and C into the first equation (A+B+C = 180)
(B-30) + B +(2B-50) = 180 Simplify and solve for B
4B-80 = 180 Add 80 to both sides.
4B = 260 Divide both sides by 4.
B = 65 degrees
A = B-30 = 65-30 = 35 degrees.
C = (A+B)-20 = 35+65-20 100 - 20 = 80 degrees.
Check:
A+B+C = 180
35+65+80 = 180
180 = 180 It checks!
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