8. Externally to an isosceles triangle $A B C$ (with $\overline{A C}=\overline{B C}$), a rhombus $B C D E$ is constructed, where $C \widehat{D} E=96^{\circ}$. What is the measure of the angle $B \widehat{A} D$?
(A) $54^{\circ}$
(B) $36^{\circ}$
(C) $42^{\circ}$
(D) $48^{\circ}$
(E) the given data is not sufficient
Problem 8. The correct answer is $(\mathbf{C})$.

The circle with center $C$ and radius $\overline{A C}=\overline{B C}=\overline{D C}$ passes through the points $A, B, D$. By the central angle theorem, $B \widehat{A} D=\frac{1}{2} B \widehat{C} D$. The angle $B \widehat{C} D$ is supplementary to $C \widehat{D} E$: it thus has a measure of $84^{\circ}$, so $B \widehat{A} D=42^{\circ}$.

![](https://cdn.mathpix.com/cropped/2024_04_17_48746ba046504379ff31g-2.jpg?height=377&width=439&top_left_y=1492&top_left_x=859)