Solve for x, y, and z.

The given triangle is isosceles, so the two remaining angles in the triangle both have measure xº. The interior angles of any triangle sum to 180º, so that

58º + xº + xº = 180º

58 + 2x = 180

2x = 122

x = 61

Angles y and z are supplementary to angle x, so that

xº + yº = 180º

and

xº + zº = 180º

and consequently, y = z. In particular, we get

y = 180 - 61

y = 119

and so

z = 119