Question

Dado que $\angle 1 + \angle 2 = 180^\circ$ $\angle 3 = \angle 4$ halla $\angle 4$ .

$\angle 1 + \angle 2 = 180^\circ$ $\angle 3 = \angle 4$ Find $\angle 4$

$20^\circ$

$25^\circ$

$30^\circ$

$35^\circ$

$40^\circ$

Solución:

Tenemos que $\angle 1 = 180^{\circ} - 70^{\circ} - 40^{\circ} = 70^{\circ}$ usando que los ángulos interiores de un triángulo suman $180^{\circ}.$

Esto nos dice que $\angle 2 = 180^{\circ} - \angle 1 = 110^{\circ}$ ya que $\angle 1$ y $\angle 2$ son suplementarios.

Finalmente, $\angle 3 + \angle 4 + 110^{\circ} = 180^{\circ} \Rightarrow$ $2 \angle 4 = 70^{\circ} \Rightarrow \angle 4 = 35^{\circ}.$

Por lo tanto, D es la respuesta correcta.

We have that $\angle 1 = 180^{\circ} - 70^{\circ} - 40^{\circ} = 70^{\circ}$ using the fact that the interior angles of a triangle add to $180^{\circ}.$

This tells us that $\angle 2 = 180^{\circ} - \angle 1 = 110^{\circ}$ since $\angle 1$ and $\angle 2$ are supplementary.

Finally, $\angle 3 + \angle 4 + 110^{\circ} = 180^{\circ} \Rightarrow$ $2 \angle 4 = 70^{\circ} \Rightarrow \angle 4 = 35^{\circ}.$

Thus, D is the correct answer.

1997 AMC 8 Problema 12

Solución:

El Problema 12 en otros años