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 $\angle CBD?$

$0$

$2$

$4$

$6$

$12$

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.