In \(\triangle{ABC}\) shown below, the measure of \(\angle{A}\) is \(58^\circ\), and \(\overline{AB} \cong \overline{AC}\). What is the measure of \(\angle{C}\) ?

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Since two sides of a triangle are congruent, we have an isosceles triangle. The angles opposite of the two congruent sides are also congruent. Therefore,

$$ x+x+58 = 180 $$ $$ 2x = 122 $$ $$ x= \boxed{61} $$