17. (★★★)如圖,在△ABC中,點D在邊BC上,點E在邊AC上,連接AD,DE,∠B=60°.
(1)若∠3=60°,試說明∠1=∠2;
(2)若∠C=40°,∠1=50°,且∠3=∠4,求∠2的度數.
答案： (1) 在$\triangle ABD$中，$\angle B = 60^{\circ}$，
$\angle 1 = 180^{\circ}-\angle B-\angle ADB = 120^{\circ}-\angle ADB$。
又$\because \angle 3 = 60^{\circ}$，
$\therefore \angle 2 = 180^{\circ}-\angle 3-\angle ADB = 120^{\circ}-\angle ADB$。
$\therefore \angle 1 = \angle 2$。
(2)$\because \angle C = 40^{\circ}$，$\angle B = 60^{\circ}$，
$\therefore \angle BAC = 180^{\circ}-\angle B-\angle C = 80^{\circ}$。
又$\because \angle 1 = 50^{\circ}$，
$\therefore \angle DAE = \angle BAC-\angle 1 = 30^{\circ}$。
又$\because \angle 3 = \angle 4$，$\angle DEC+\angle 3+\angle 4 = 180^{\circ}$，
$\therefore \angle 4 = 75^{\circ}$，
$\therefore \angle DEC = 180^{\circ}-\angle 4 = 105^{\circ}$，
$\therefore \angle 2 = 180^{\circ}-\angle DEC-\angle C = 35^{\circ}$。
