Question

已知求 $\angle 4$ 。 $\angle 1 + \angle 2 = 180^\circ$ $\angle 3 = \angle 4$

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

$20^\circ$

$25^\circ$

$30^\circ$

$35^\circ$

$40^\circ$

答案：D

知识点：导角角度和

难度评级：1170

解答：

由三角形内角和，因为三角形内角和为 $180^{\circ}$ 。 $\angle 1 = 180^{\circ} - 70^{\circ} - 40^{\circ} = 70^{\circ}$

因为 $\angle 1$ 和 $\angle 2$ 互补，所以。 $\angle 2 = 180^{\circ} - \angle 1 = 110^{\circ}$

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

所以正确答案是 D。

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 第 12 题

答案：D

难度评级：1170

解答：

其他年份的第 12 题