In the diagram, $B C D$ is a straight line segment. The measure of $\angle A B C$ is
(A) $35^{\circ}$
(B) $40^{\circ}$
(C) $60^{\circ}$
(D) $75^{\circ}$
(E) $45^{\circ}$

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-003.jpg?height=260&width=350&top_left_y=618&top_left_x=1321)
Since $B C D$ is a straight line segment, then $\angle B C D=180^{\circ}$.

Therefore, $\angle A C B=\angle B C D-\angle A C D=180^{\circ}-75^{\circ}=105^{\circ}$.

Since the sum of the three angles in $\triangle A B C$ is $180^{\circ}$, then $\angle A B C=180^{\circ}-105^{\circ}-35^{\circ}=40^{\circ}$.

ANSWER: (B)