Expert: Scott A Wilson - 6/18/2010

Question
determine the angles of an isoceles triangle if double the sum of the two equeal angles is equal to 3 times the 3rd angle

Answer
The angles of a triangle are A, B, and C.
It is knowm that A+B+C=180°.
The problem states that 2(A+B)=3C.
It also states that the triangle is isoceles, so either A=B or A=C.

For A=B, we have 2A+C=180° and 2(2A) = 3C.  The second equation is really 4A = 3C,
which means C = 4A/3.  Putting this into 2A+C=180° gives 2A + 4A/3 = 180, so 10A/3 = 180,
so multiply both sides by 3/10 to get A = 54.  This means B = 54, and C is 180-54-54=72.

For A=C, this gives the equations 2A+B=180° and 2(A+B)=A.  The 2nd equation says that
2A + 2B = A.  Subtracting 2A from both sides gives 2B = -A.  This makes no sense in the physical, for angles always have a positive value.  If this problem is with respect to direction of angles, it can be solved, since usually counterclockwise is a positive angle and clockwise is a negative angle, but that is used in higer math.