Expert: Scott A Wilson - 2/9/2011

Question
The measure of the largest angle of a triangle is 45 degrees more than the measure of the smallest angle.  The middle angle measures 6 degrees.  What is the measure of the smallest angle?

Answer
Are you sure that 6 is not suppose to be a 60?
If it were a 6, it would not be the middle size angle, so I'll go with that.
Or, on the other hand, we'll say the middle angle is x.
Call the large angle L and the small angle S.

It is known that L+S+x = 180.  From here, since x is known, it can be said L+S = 180-x.
Since L = S + 45, that is the same as 2S + 45 = 180-x.

Subtracting 45 from both sides gives 2S = 135-x.
Dividing both sides by 2 gives S = (135-x)/2.
In the last paragraph, once S has been found, it gives an equation for L from S.