SOLUTION: When the measures of the angles of a triangle are placed in order, the difference between the middle angle and smallest angle is equal to the difference between the middle angle an

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Question 1022128: When the measures of the angles of a triangle are placed in order, the difference between the middle angle and smallest angle is equal to the difference between the middle angle and largest angle. If one of the angles of the triangle has measure 23 degress then what is the measure in degrees of the largest angle of the triangle?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) (Show Source):
You can put this solution on YOUR website!
x, y, z, in that order by size;

You can try starting with x=23, and see what you find for y and z.

,
and

,
and use the system trying to solve .
-
Using elimination, adding corresponding members,
, which seems good.

z should be or .

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!

When the measures of the angles of a triangle are placed in order, the difference between the middle angle and smallest angle is equal to the difference between the middle angle and largest angle. If one of the angles of the triangle has measure 23 degress then what is the measure in degrees of the largest angle of the triangle?

Let largest, middle, and smallest angles, be L, M, and S, respectively
We then get: M - S = L - M______L - 2M + S = 0 ------- eq (i)
Also, L + M + S = 180 ------- eq (ii)
- 3M = - 180 ------ Subtracting eq (ii) from eq (i)
M, or middle angle = , or
It's obvious that COULD NEVER be the largest angle, so now that we know the middle angle, is the smallest angle
Therefore, L, or largest angle = 180 - (60 + 23), or 180 - 83, or