a) Ta có:
$\widehat{A} + \widehat{B} + \widehat{C} + \widehat{D} = 360^o$
$\Leftrightarrow \widehat{A} + \widehat{B} + 60^o + 80^o = 360^o$
$\Leftrightarrow \widehat{A} + \widehat{B} = 220^o$
$\Leftrightarrow \widehat{A} = 220^o - \widehat{B}$
Ta lại có:
$\widehat{A} - \widehat{B} = 10^o$
$\Rightarrow 220^o - \widehat{B} - \widehat{B} = 10^o$
$\Leftrightarrow 2\widehat{B} = 210^o$
$\Leftrightarrow \widehat{B} =105^o$
$\Rightarrow \widehat{A} = 115^o$
Bài 2:
Ta có:
$AB = AC \quad (gt)$
$BM = CN\quad (gt)$
$\Rightarrow AB - BM = AC - CN$
$\Rightarrow AM= AN$
$\Rightarrow \dfrac{AM}{AB} =\dfrac{AN}{AC}$
Xét $ΔAMN$ và $ΔABC$ có:
$\dfrac{AM}{AB} =\dfrac{AN}{AC}$
$\widehat{A}:$ góc chung
Do đó $ΔAMN\sim ΔABC\, (c.g.c)$
$\Rightarrow \widehat{AMN} = \widehat{ABC}$
$\Rightarrow MN//BC$
$\Rightarrow BMNC$ là hình thang
Lại có: $\widehat{B} = \widehat{C}$ ($ΔABC$ cân tại $A$)
$\Rightarrow BMNC$ là hình thang cân
