SOLUTION: Trying to help our daughter... In an obtuse scalene triangle, one angle is 70 degrees larger than another angle and the thrid angle is half the sum of the other two angles. What i

Algebra ->  Triangles -> SOLUTION: Trying to help our daughter... In an obtuse scalene triangle, one angle is 70 degrees larger than another angle and the thrid angle is half the sum of the other two angles. What i      Log On


   

Question 958908: Trying to help our daughter...
In an obtuse scalene triangle, one angle is 70 degrees larger than another angle and the thrid angle is half the sum of the other two angles. What is the measure, in degrees, of each of the three angles of the triangle?
Thank you!
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Sort through the description and transcribe into number expressions. Assign some variables; your choice how...

"one angle", 70 degrees more than...?.
"another angle", x
"the third angle", y

"one angle", 70%2Bx;
"third angle", y=%281%2F2%29%28%2870%2Bx%29%2Bx%29

Review all that and find how it makes sense before continuing...


Simplify the "third angle" equation.
y=%281%2F2%29%2870%2B2x%29
highlight_green%28y=35%2Bx%29


If you wonder what to do next having only one equation in two unknown variables, use the fact for sum of interior angles of a triangle: 180 degrees.

%2870%2Bx%29%2Bx%2By=180, now giving you TWO equations in two unknown variables.

Simplifying, 70%2B2x%2By=180
highlight_green%282x%2By=110%29

You have a system,
highlight%28system%28y=35%2Bx%2C2x%2By=110%29%29
which should be a simple chore to solve and no further trouble.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Trying to help our daughter...
In an obtuse scalene triangle, one angle is 70 degrees larger than another angle and the thrid angle is half the sum of the other two angles. What is the measure, in degrees, of each of the three angles of the triangle?
Thank you!
Using ONE variable will work perfectly fine

Let measure of 2nd angle be S

Then measure of 1st angle = S + 70

And, 3rd angle = %281%2F2%29%28S+%2B+S+%2B+70%29_______%281%2F2%29%282S+%2B+70%29_______%282S+%2B+70%29%2F2______2%28S+%2B+35%29%2F2______cross%282%29%28S+%2B+35%29%2Fcross%282%29, or S + 35

As these are angles of a TRIANGLE. we get: S + S + 70 + S + 35 = 180

3S + 105 = 180

3S = 180 – 105

3S = 75

S, or measure of 2nd angle = 75%2F3, or highlight_green%2825%5Eo%29

Measure of 1st angle: 25 + 70, or highlight_green%2895%5Eo%29 

Measure of 3rd angle: 25 + 35, or highlight_green%2860%5Eo%29