Answer:
![\text{A. }32^(\circ)](https://img.qammunity.org/2022/formulas/mathematics/college/7dp67aqjduvqzoiksdgow59l7ec85nfzfm.png)
Explanation:
From the Isosceles Base Theorem, the two base angles of a isosceles triangle are equal. Therefore,
.
Since the sum of the interior angles of a triangle is always equal to 180 degrees, we can write the following equation:
![\angle A+\angle B+\angle C=180](https://img.qammunity.org/2022/formulas/mathematics/college/qy50gz4hsqxiu4pl54mzxy5osgpiqiyfer.png)
Substitute
into this equation to solve for
:
![74+\angle B+74=180,\\\angle B=180-74-74=\boxed{32^(\circ)}](https://img.qammunity.org/2022/formulas/mathematics/college/22m3hqeglvpugdl8g969w7p4zsh9rmxo6u.png)