Question

角 $A$ 的度数是

The degree measure of angle $A$ is

$20$

$30$

$35$

$40$

$45$

答案：B

知识点：导角

难度评级：1520

解答：

如下标记顶点。

由补角关系，同样由补角关系，利用三角形内角和为 $180^{\circ}$ ，得到再由对顶角相等，最后在三角形中使用内角和，得到 $\angle ABC = 180^{\circ} - 100^{\circ} = 80^{\circ}$ $\angle CED = 180^{\circ} - 110^{\circ} = 70^{\circ}$ $\angle ECD = 180^{\circ} - 70^{\circ} - 40^{\circ}$ $= 70^{\circ}.$ $\angle ACB = \angle ECD = 70^{\circ}.$ $\angle A = 180^{\circ} - 80^{\circ} - 70^{\circ} = 30^{\circ}.$

所以正确答案是 B。

Label the vertices as below.

We then have that $\angle ABC = 180^{\circ} - 100^{\circ} = 80^{\circ}$ by supplementary angles. Then we have $\angle CED = 180^{\circ} - 110^{\circ} = 70^{\circ}$ again by supplementary angles. Using the sum of the interior angles of a triangle is $180^{\circ},$ we get $\angle ECD = 180^{\circ} - 70^{\circ} - 40^{\circ}$ $= 70^{\circ}.$ Then, using vertical angles, we have $\angle ACB = \angle ECD = 70^{\circ}.$ Finally, using the sum of the interior angles of a triangle, we get $\angle A = 180^{\circ} - 80^{\circ} - 70^{\circ} = 30^{\circ}.$

Thus, B is the correct answer.

1999 AMC 8 第 21 题

答案：B

难度评级：1520

解答：

其他年份的第 21 题