Giải câu 5 trang 112 sách phát triển năng lực toán 7 tập 1.
Tam giác ABC có:
$\widehat{A}$ + $\widehat{B}$ + $\widehat{C}$ = 180$^{\circ}$
a. $\widehat{A}$ + $\widehat{B}$ = $\widehat{C}$
$\Rightarrow $ $\widehat{A}$ + $\widehat{B}$ = $\widehat{C}$ = $\frac{1}{2}$.180$^{\circ}$ = 90$^{\circ}$
Mà $\widehat{A}$ - $\widehat{B}$ = 30$^{\circ}$ $\Rightarrow $ $\widehat{A}$ = 60$^{\circ}$; $\widehat{B}$ = 30$^{\circ}$
b. 4$\widehat{A}$ = 6$\widehat{B}$ = 3$\widehat{C}$
$\Rightarrow $$\frac{\widehat{A}}{\frac{1}{4}}=\frac{\widehat{B}}{\frac{1}{6}}=\frac{\widehat{C}}{\frac{1}{3}}=\frac{\widehat{A}+\widehat{B}+\widehat{C}}{\frac{1}{4}+\frac{1}{6}+\frac{1}{3}}=\frac{180^{\circ}}{\frac{3}{4}}= 240^{\circ}$
$\Rightarrow $ $\widehat{A}$ = $60^{\circ}$; $\widehat{B}$ = $40^{\circ}$; $\widehat{C}$ = $80^{\circ}$
c. 2$\widehat{A}$ = 3$\widehat{B}$; 4$\widehat{A}$ + 3$\widehat{B}$ = 180$^{\circ}$
$\Rightarrow 2\widehat{A}+4\widehat{A}=180^{\circ}$
$\Rightarrow \widehat{A} = 30^{\circ}; \widehat{B} = 20^{\circ}$
$\Rightarrow \widehat{C} = 180^{\circ} - \widehat{A} - \widehat{B} = 180^{\circ}-20^{\circ}-30^{\circ}=130^{\circ}$