初中数学八年级上册试题库（555题）

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求∠EAD的度数。

知识点：第十一章　三角形

参考答案：20°（1）\(\because \angle B = 40^\circ \)，\(\angle ACB = 80^\circ \)，\(\therefore \angle BAC = 180^\circ - 40^\circ - 80^\circ = 60^\circ \)，\(\because AE\)是\(\Delta ABC\)的角平分线，\(\therefore \angle BAE = \frac{1}{2}\angle BAC = 30^\circ \)，\(\because FG \bot AE\)，\(\therefore \angle AHG = 90^\circ \)，\(\therefore \angle AGF = 180^\circ - 90^\circ - 30^\circ = 60^\circ \)；（2）\(\because AD\)是\(\Delta ABC\)的高，\(\therefore \angle ADC = 90^\circ \)，\(\because \angle ACB = 80^\circ \)，\(\therefore \angle CAD = 180^\circ - 90^\circ - 80^\circ = 10^\circ \)，\(\because \angle BAC = 60^\circ \)，\(AE\)是\(\Delta ABC\)的角平分线，\(\therefore \angle CAE = \frac{1}{2}\angle BAC = 30^\circ \)，\(\therefore \angle EAD = \angle CAE - \angle CAD = 30^\circ - 10^\circ = 20^\circ \)．