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Question 1124989: 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 Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let the angles be A,B,C.
the sum of the angles is 180 degrees, therefore A + B + C = 180.
the second angle measures 20 degrees more than the first, therefore B = A + 20.
the third angle measures 35 degrees more than the second, therefore C = B + 35.
since B = A + 20, then replace B in C = B + 35 to get C = A + 20 + 35.
you now have:
B = A + 20
C = A + 55
the sum of (A,B,C) = 180
in this equation, replace B with A + 20 and C with A + 55 to get:
A + A + 20 + A + 55 = 180
combine like terms to get:
3A + 75 = 180
subtract 75 from both sides of this equation to get:
3A = 105
solve for A to get:
A = 105 / 3 = 35
you get:
A = 35
B = A + 20 = 55
C = A + 55 = 90
A + B + C = 35 + 55 + 90 = 180.
B = A + 20 = 35 + 20 = 55
C = B + 35 = 55 + 35 = 90
everything chcks out so the solution looks good.
the solution is that the measure of each angle is {35, 55, 90}.
Answer by MathTherapy(10552)  (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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