SOLUTION: 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 t

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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!