Question 65834
Alright ... the Triangle on the left is Isocoles.  The two base angles (we will label them 'y' ) are equal.  So if the top angle is 58 deg, then the bottom two are each equal 61 deg.
{{{ y+y+58=180 }}}
{{{2y + 58 = 180 }}}
{{{ 2y = 122 }}}
{{{ y = 61 }}}


In the triangle on the right ... the angle that is next to the 61 deg angle is 119 deg, because it is the supplement to the other angle, and they make a linear pair. (label this one 'z' )
{{{ 61 + z = 180 }}}
{{{ z = 119 }}}


Still looking at the Triangle on the right, the angle measuring 119 is the vertex of yet another isocoles triangle which means the other two are congruent.
{{{ x+x+119 = 180 }}}
{{{ 2x + 119 = 180 }}}
{{{ 2x = 61 }}}
{{{ x = 30.5 }}}


Here is your check:
{{{ x + (58+x) + y = 180 }}}
This is the LARGE triangle.
{{{ 30.5 + 58 + 30.5 + 61 = 180 }}}
{{{ 88.5 + 30.5 + 61 = 180 }}}
{{{ 119 + 61 = 180 }}}
{{{ 180 = 180 }}}
YES!!!