Question

Sean

\angle ABC = 24^\circ

y

\angle ABD = 20^\circ .

¿Cuál es la menor medida en grados posible para

\angle CBD

?

Let

\angle ABC = 24^\circ

and

\angle ABD = 20^\circ .

What is the smallest possible degree measure for

\angle CBD?

0

2

4

6

12

Ambos ángulos comparten el rayo

BA

.

Both angles share ray

BA

El ángulo más pequeño ocurre cuando los dos ángulos dados se superponen lo máximo posible.

The smallest angle occurs when the two given angles overlap as much as possible

Observa que ambos ángulos comparten el rayo

AB.

Para minimizar el grado deseado, queremos que

D

esté entre

A

y

C.

Esto daría

\begin{aligned} \angle CBD &= \angle ABC - \angle ABD \\ &= 4^{\circ}. \end{aligned}

Por lo tanto, C es la respuesta correcta.

Note that both of the angles share the ray

AB.

To minimize the desired degree, we want

D

to be between

A

and

C.

This would make

\begin{aligned} \angle CBD &= \angle ABC - \angle ABD \\ &= 4^{\circ}. \end{aligned}

Thus, C is the correct answer.