Đáp án:
$a)\widehat{A}=70^\circ;\widehat{B}=120^\circ;\widehat{C}=50^\circ\\ b)\widehat{A}=60^\circ; \widehat{C}=40^\circ;\widehat{B}=80^\circ\\ c)\widehat{A}=40^\circ;\widehat{B}=60^\circ;\widehat{C}=80^\circ$
Giải thích các bước giải:
$a)\widehat{A}=70^\circ; \widehat{B}-\widehat{C}=10^\circ(1)$
ABC là tam giác $\Rightarrow \widehat{A}+\widehat{B}+\widehat{C}=180^\circ$
$\Rightarrow \widehat{B}+\widehat{C}=180^\circ-\widehat{A}=110^\circ\\ \Leftrightarrow \widehat{B}+\widehat{C}=110^\circ(2)$
Cộng 2 vế của $(1)(2)$ ta được $2\widehat{B}=120^\circ$
$\Leftrightarrow \widehat{B}=60^\circ\\ \Rightarrow \widehat{C}=50^\circ\\ b)\widehat{A}=60^\circ; \widehat{B}=2\widehat{C}$
ABC là tam giác $\Rightarrow \widehat{A}+\widehat{B}+\widehat{C}=180^\circ$
$\Leftrightarrow\widehat{A}+2\widehat{C}+\widehat{C}=180^\circ\\ \Leftrightarrow 60^\circ+3\widehat{C}=180^\circ\\ \Leftrightarrow 3\widehat{C}=120^\circ\\ \Leftrightarrow \widehat{C}=40^\circ\\ \Rightarrow \widehat{B}=2\widehat{C}=80^\circ\\ c)\widehat{A}:\widehat{B}:\widehat{C}=2:3:4\\ \Rightarrow \dfrac{\widehat{A}}{2}=\dfrac{\widehat{B}}{3}=\dfrac{\widehat{C}}{4}$
Đặt $\dfrac{\widehat{A}}{2}=\dfrac{\widehat{B}}{3}=\dfrac{\widehat{C}}{4}=k$
$\Rightarrow \widehat{A}=2k;\widehat{B}=3k;\widehat{C}=4k$
$ABC$ là tam giác $\Rightarrow \widehat{A}+\widehat{B}+\widehat{C}=180^\circ$
$\Leftrightarrow 2k+3k+4k=180^\circ\\ \Leftrightarrow 9k=180^\circ\\ \Leftrightarrow k=20^\circ\\ \Rightarrow \widehat{A}=40^\circ;\widehat{B}=60^\circ;\widehat{C}=80^\circ$
