SOLUTION: We know from geometry that the sum of the angles in any triangle is 180 degrees. suppose that the smallest angel is 78 degrees less than the largest one. Also suppose that the midd

Question 347916: We know from geometry that the sum of the angles in any triangle is 180 degrees. suppose that the smallest angel is 78 degrees less than the largest one. Also suppose that the middle angle is three times as large as the smallest angle. What is the degree measure of each angle. Thank you
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
We know from geometry that the sum of the angles in any triangle is 180 degrees.
suppose that the smallest angel is 78 degrees less than the largest one.
Also suppose that the middle angle is three times as large as the smallest angle.
What is the degree measure of each angle
:
Let the three angle be A, B, C, (A is the largest, C is the smallest)
:
Write an equation for each statement:
"the smallest angel is 78 degrees less than the largest one."
C = A - 78)
or if you add 78 to both sides:
A = (C+78)
:
"the middle angle is three times as large as the smallest angle."
B = 3C
:
A + B + C = 180
Replace A with (C+78); Replace B with 3C
(C+78) + 3C + C = 180
5C = 180 - 78
5C = 102
C =
C = 20.4 degrees is the smallest angle
then
A = 20.4 + 78
A = 98.4 degrees is the largest angle
and
B = 3(20.4)
B = 61.2 degrees is the middle angle
;
:
Check our solutions by finding the sum of the angles
98.4 + 61.2 + 20.4 = 180; confirms our solutions

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