Question 994095: The measure of the largest angle of a triangle is 10 degrees more than the sum of the measures of the other two angles and 10 degrees less than 3 times the measure of the smallest angle. Find the measures of the three angles of the triangle.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The measure of the largest angle of a triangle is 10 degrees more than the sum of the measures of the other two angles and 10 degrees less than 3 times the measure of the smallest angle.
Find the measures of the three angles of the triangle.
:
let the 3 angles be A, B, C, with A being the largest
:
"The measure of the largest angle of a triangle is 10 degrees more than the sum of the measures of the other two angles"
A = B + C + 10
" and 10 degrees less than 3 times the measure of the smallest angle.
A = 3C - 10
We also know that
A + B + C = 180
Rewrite the 1st equation and add to the above equation
A + B + C = 180
A - B - C = 10
--------------------Adding eliminates B and C, find A
2A + 0 + 0 = 190
A = 190/2
A = 95 degrees
Find C using the 2nd equation
A = 3C - 10
95 = 3C - 10
95 + 10 = 3C
105 = 3C
C = 105/3
C = 35 degrees
Find B
95 + B + 35 = 180
B + 130 = 180
B = 180 - 130
B = 50 degrees
:
the measures of the three angles: 95, 50, 35
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