SOLUTION: the second angle of a triangle is 10 degrees less than three times the first angle. The third angle is 10 degrees less than the second angle. find the angles of this triangle

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Question 149073: the second angle of a triangle is 10 degrees less than three times the first angle. The third angle is 10 degrees less than the second angle. find the angles of this triangle
Answer by nabla(475) About Me  (Show Source):
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let angle 1 = a
angle 2= b
angle 3=c

a=a
b=3a-10
c=b-10

THEN
a=a
b=3a-10
c=3a-10-10
THEN
a=a
b=3a-10
c=3a-20
AND
a+b+c=180 (BECAUSE of the definition of a triangle having 180 degrees total angle measure)
SO
a+3a-10+3a-20=180
7a-30=180
7a=210
a=30.
So b=80 and c=70.
Angles are 30, 70, and 80.