Question

Two angles of an isosceles triangle measure 69 degrees and x degrees. What is the sum of all possible values of x?

Answer 1

69 +2x =180
2x = 111
x = 55.5 degrees

If 69 and x are equal angles, x=69.

if x isthe third angle, x = 180-138 =42
Therefore sum is 69+55.5+42 = 166.5 degrres

Answer 2

In any isosceles triangle angles opposite to the congruents sides are also congruent.So any two angles in  this triangle must be equal.
The three possibilities are:
1. the 69 degrees and x degrees are congruent angles.
2. There are two 69 degree angles. Sum equals 69+69=138
Since, the sum of the three angles=180
69+69+x=180
x=180-138=42 degrees
3. Other possibility is , there are two angles of x degrees, then
x+x+69=180
2x+69=180
2x=111
x=55.5 degrees
The sum of all these possibilities = 69+42+55.5=166.5