Question 118610
Remember, in any triangle, the sum of all three angles is 180 degrees. Also, if angle x is the vertex angle and angles y and z are the base angles (these angles are equal ie {{{y=z}}}), 


So the sum of the three angles is represented by this equation:

{{{x+y+z=180}}}


{{{x+z+z=180}}} Now plug in {{{y=z}}}



{{{x+2z=180}}} Combine like terms


Since we know that the vertex angle of the isosceles triangle is 64 degrees, this means {{{x=64}}}


{{{64+2z=180}}} Now plug in  {{{x=64}}} into the equation




{{{2z=180-64}}}Subtract 64 from both sides



{{{2z=116}}} Combine like terms on the right side



{{{z=(116)/(2)}}} Divide both sides by 2 to isolate y




{{{z=58}}} Divide



So the base angles are both 58 degrees