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?
<pre>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 = {{{(- 180)/(- 3)}}}, or {{{60^o}}}
It's obvious that {{{23^o}}} COULD NEVER be the largest angle, so now that we know the middle angle, {{{23^o}}} is the smallest angle
Therefore, L, or largest angle = 180 - (60 + 23), or 180 - 83, or {{{highlight_green(97^o)}}}