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Question 1124988: The sum of the measures of the three angles of a triangle is equal to 180 degrees. In a given triangle, the second angle measures 20 degrees more than the first and the third, 35 degrees more than the second. What is the measure of each of these angles?
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Three angles A,B,C; write an equation for each statement
:
The sum of the measures of the three angles of a triangle is equal to 180 degrees.
A + B + C = 180
In a given triangle, the second angle measures 20 degrees more than the first
B = A + 20
or
A = B - 20
and the third, 35 degrees more than the second.
C = B + 35
:
What is the measure of each of these angles?
In the 1st equation, replace A with (B-20) and replace C with (B+35)
(B-20) + B + (B+35) = 180
combine like terms
B + B + B - 20 + 35 = 180
3B + 15 = 180
3B = 180 - 15
3B = 165
B = 165/3
B = 55 degrees
:
I'll let you find A & C using the equations we have for each statement
Ensure that the 3 angles do indeed, add up to 180
Answer by MathTherapy(10551)  (Show Source):
You can put this solution on YOUR website!
The sum of the measures of the three angles of a triangle is equal to 180 degrees. In a given triangle, the second angle measures 20 degrees more than the first and the third, 35 degrees more than the second. What is the measure of each of these angles?
Let the measure of the first angle be F
Then the second angle = F + 20
And, the third = F + 20 + 35 = F + 55
We then get: F + F + 20 + F + 55 = 180
3F + 75 = 180
3F = 105
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