Polygons and Circles Question 1

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

32^\circ

42^\circ

58^\circ

61^\circ

62^\circ

Approach

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}