4.7. Hãy viết các góc $\widehat{A},\widehat{B},\widehat{C}$ của tam giác ABC theo thứ tự giảm dần các trường hợp sau:
a)$\widehat{A}=60^{\circ},\widehat{B}<\widehat{A}$.
b)$\widehat{A}>90^{\circ},\widehat{B}>45^{\circ}$.
Bài Làm:
a) Ta có: $\widehat{A}+\widehat{B}+\widehat{C}=180 ^{\circ}=> \widehat{B}+\widehat{C}=180^{\circ}-\widehat{A}=180^{\circ}-60^{\circ}=120^{\circ}$.
Vì $\widehat{B}<\widehat{A}=60^{\circ}$ nên $\widehat{C}>60^{\circ}$. Như vậy $\widehat{C}>\widehat{A}>\widehat{B}$.
b) Ta có: $\widehat{A}+\widehat{B}+\widehat{C}=180^{\circ}$ => $\widehat{C}=180^{\circ}-\widehat{A}-\widehat{B}<45^{\circ}<\widehat{B}$.
Mặt khác, $\widehat{B}=180^{\circ}-\widehat{A}-\widehat{C}<180^{\circ}-\widehat{A}<90^{\circ}<\widehat{A}$.
Như vậy $\widehat{A}>\widehat{B}>\widehat{C}$.