Bài 3:
a) Xét ΔABC có:
$\widehat{A}+\widehat{B}+\widehat{C}=180^0$
Thay $\widehat{A}+70^0+30^0=180^0$
$⇔ \widehat{A}=80^0$
Mà AD là phân giác của góc A
$⇒\widehat{A_1}=\widehat{A_2}=$$\frac{\widehat{A}}{2}=$ $\frac{80^0}{2}=40^0$
Xét ΔADC có:
$\widehat{A_1}+\widehat{D_1}+\widehat{C}=180^0$
$40^0+\widehat{D_1}+30^0=180^0$
$\widehat{D_1}=110^0$
Bài 4:
a) Xét $ΔACE$ có $\widehat{E}=90^0⇒\widehat{C_1}+\widehat{A}=90^0$
Xét $ΔABD$ có $\widehat{D}=90^0⇒\widehat{B_1}+\widehat{A}=90^0$
$⇒\widehat{B_1}=\widehat{C_1}$
$⇒∠ABD=∠ACE$
b) Xét tứ giác AEHD có $\widehat{HEA}+\widehat{A}+\widehat{ADH}+\widehat{DHE}=360^0$
$⇒\widehat{EHD}+\widehat{A}=360^0-(\widehat{AEH}+\widehat{HDA})=360^0-(90^0+90^0)=180^0$
$⇒∠A+∠DHE=180^0$
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