Gọi số đo góc A,B,C lần lượt là x,y,z ( x,y,z là các số dương < 180 )
Ta có:\(x+y+z=180^0\)
\(\Leftrightarrow5z+3z+z=180^0\)
\(\Leftrightarrow9z=180^0\Rightarrow z=20^0\Rightarrow x=100^0;y=60^0\)
Theo bài ta có: \(\widehat{A}=5\widehat{C}\)\(\Rightarrow\frac{\widehat{A}}{5}=\widehat{C}\)(1)
\(\widehat{B}=3\widehat{C}\)\(\Rightarrow\frac{\widehat{B}}{3}=\widehat{C}\)(2)
Từ (1) và (2) \(\Rightarrow\frac{\widehat{A}}{5}=\frac{\widehat{B}}{3}=\widehat{C}=\frac{\widehat{A}+\widehat{B}+\widehat{C}}{5+3+1}=\frac{180^o}{9}=20^o\)
\(\Rightarrow\widehat{A}=20^o.5=100^o\); \(\widehat{B}=20^o.3=60^o\); \(\widehat{C}=20^o.1=20^o\)
Vậy \(\widehat{A}=100^o\), \(\widehat{B}=60^o\); \(\widehat{C}=20^o\)
