SOLUTION: The measure of the largest angle of a triangle is 12 degree less than the sum of the measure of the other two. The smallest angle measures 58 degrees less than the largest. Find th

Question 163820: The measure of the largest angle of a triangle is 12 degree less than the sum of the measure of the other two. The smallest angle measures 58 degrees less than the largest. Find the measures of the angles.
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 12 degree less than the sum of the measure of the other two. The smallest angle measures 58 degrees less than the largest. Find the measures of the angles.
:
The three angles, A, B, C (A is the largest)
:
"The measure of the largest angle of a triangle is 12 degree less than the sum of the measure of the other two."
A = B + C - 12
:
" The smallest angle measures 58 degrees less than the largest."
C = A-58
:
We have a 3rd equation we can use:
A + B + C = 180
:
Find the measures of the angles.
;
rearrange the 1st equation to, add to the 3rd equation. Find A:
A - B - C = -12
A + B + C = 180
------------------adding eliminates B & C
2A = 168
A =
A = 84 degrees
:
We have the given equation: C = A - 58
C = 84 - 58
C = 26 degrees
:
I'll let you find B
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