In the diagram, $A B C D$ is a rhombus. The size of $\angle B C D$ is
(A) $60^{\circ}$
(D) $45^{\circ}$
(B) $90^{\circ}$
(C) $120^{\circ}$
(E) $160^{\circ}$

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-092.jpg?height=287&width=409&top_left_y=1098&top_left_x=1346)
In the diagram, $A B C D$ is a rhombus. The size of $\angle B C D$ is
(A) $60^{\circ}$
(B) $90^{\circ}$
(C) $120^{\circ}$
(D) $45^{\circ}$
(E) $160^{\circ}$

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-402.jpg?height=298&width=410&top_left_y=594&top_left_x=1367)

## Solution

We are given that $\triangle A D C$ is equilateral which means that $\angle D A C=\angle A C D=\angle A D C=60^{\circ}$. Similarly, each of the angles in $\triangle A B C$ equals $60^{\circ}$. This implies that $\angle B C D$ equals $120^{\circ}$ since $\angle B C D=\angle B C A+\angle D C A$ and $\angle B C A=\angle D C A=60^{\circ}$.