SOLUTION: Two angles of an isosceles triangle measure 69o and xo. What is the sum of all possible values of x? ___________ ___________ ___________ ____ Select one option 55.5 124

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Question 818179: Two angles of an isosceles triangle measure 69o and xo. What is the sum of all possible values of x?
________________________________________
Select one option

55.5

124.5

166.5

69
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
In any isosceles triangle the angles opposite the the congruent sides are also congruent. So two of the angles in this triangle must be equal. There are three possibilities:
  • The 69 degree and the x degree angles are the congruent ones. In this case x = 69.
  • There are two 69 degree angles. Since 69+69 = 138 and since the three angles must add up to 180 degrees, the remaining angle, x, is 180-138 = 42 degrees.
  • There are two angles of x degrees. Then
    x + x + 69 = 180.
    Solving this:
    2x + 69 = 180
    2x = 180-69 = 111
    x = 111/2 = 55.5
The sum of all these possibilities is:
69 + 42 + 55.5 = 166.5