Đáp án:
$\widehat{A}=\widehat{B}= 108^\circ$
$\widehat{C}=\widehat{D}=72^\circ$
Giải thích các bước giải:
Ta có:
$\triangle ABC$ cân tại $B$
$\Rightarrow \widehat{BAC}=\widehat{BCA}$
Lại có:
$\widehat{BAC}=\widehat{DCA}$ (so le trong)
Do đó:
$\widehat{BCA}=\widehat{DCA}$
$\Rightarrow \widehat{DCA}=\dfrac12\widehat{BCD}$
$\Rightarrow \widehat{DCA}=\dfrac12\widehat{ADC}$
Xét $\triangle ACD$ cân tại $C$ có:
$\quad \widehat{DCA}= 180^\circ - 2\widehat{ADC}$
$\Leftrightarrow \dfrac12\widehat{ADC}= 180^\circ - 2\widehat{ADC}$
$\Leftrightarrow \dfrac52\widehat{ADC}= 180^\circ$
$\Leftrightarrow \widehat{ADC}= 72^\circ$
Khi đó:
$\bullet\quad \widehat{BCD}=\widehat{ADC}= 72^\circ$
$\bullet\quad \widehat{CBA}=\widehat{DAB}= 180^\circ - \widehat{ADC}= 108^\circ$
