3) If it is known that in the adjacent figure $C \widehat{A} E=60^{\circ}$, $A \widehat{E} B=20^{\circ}, A \widehat{C} D=25^{\circ}$. The points $E, D, B$ are collinear. What is the measure of $B \widehat{D} C$?
(A) $75^{\circ}$
(B) $85^{\circ}$
(C) $90^{\circ}$
(D) $105^{\circ}$
(E) the information is insufficient

![](https://cdn.mathpix.com/cropped/2024_04_17_58bef2a2a14f9f84b61bg-1.jpg?height=75&width=466&top_left_y=1704&top_left_x=959)
3) The answer is $\mathbf{( A )}$.

The angle $D \widehat{B} C$, by the exterior angle theorem, is

$$
B \widehat{A} E+A \widehat{E} B=60^{\circ}+20^{\circ}=80^{\circ} .
$$

It follows that

$$
B \widehat{D} C=180^{\circ}-D \widehat{B} C-B \widehat{C} D=180^{\circ}-80^{\circ}-25^{\circ}=75^{\circ} \text {. }
$$