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\(\text{Theo định lí tổng 3 góc của 1 tam giác ta có:}\)
\(\text{góc A+góc B +góc C =180}\)
\(\text{Mà góc B=2 góc C nên:}\)
\(\text{góc A+2 góc C + góc C =180}\)
=>30\(\text{+3 góc C =180}\)
=>3 góc C = 150
=> góc C =50
Xét \(\Delta ABC\)có:
\(\widehat{A}+\widehat{B}+\widehat{C}=180^o\)(ĐL tổng 3 góc trong tam giác)
\(\Rightarrow30^o+\widehat{B}+\widehat{C}=180^o\)
\(\Rightarrow\widehat{B}+\widehat{C}=180^o-30^o=150^o\)
Mà \(\widehat{B}=2\widehat{C}\)
\(\Rightarrow\widehat{B}=150^o:\left(1+2\right)\cdot2=100\)
\(\Rightarrow\widehat{C}=150^o-100^o=50^o\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Do ∆ABC cân tại A=> góc B= góc C
Mà góc A=50°=> góc B=góc C= (180°-50°)/2=65°
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\widehat{AEB}=\widehat{EBC}+\widehat{C}\)
\(\Leftrightarrow\widehat{ABE}-\widehat{EBC}=\widehat{B}-20^0\)
\(\Leftrightarrow\widehat{ABE}-\widehat{EBC}-\widehat{ABE}-\widehat{EBC}=-20^0\)
\(\Leftrightarrow\widehat{EBC}=10^0\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
Câu 1:
Giải:
Ta có: \(15x=\left(-10\right)y=6z\Rightarrow\frac{15x}{30}=\frac{\left(-10\right)y}{30}=\frac{6z}{30}\Rightarrow\frac{x}{2}=\frac{y}{-3}=\frac{z}{5}\)
Đặt \(\frac{x}{2}=\frac{y}{-3}=\frac{z}{5}=k\)
\(\Rightarrow x=2k,y=-3k,z=5k\)
Mà \(xyz=-30000\)
\(\Rightarrow2k\left(-3\right)k5k=-30000\)
\(\Rightarrow\left(-30\right).k^3=-30000\)
\(\Rightarrow k^3=1000\)
\(\Rightarrow k=10\)
\(\Rightarrow x=20;y=-30;z=50\)
Vậy bộ số \(\left(x;y;z\right)\) là \(\left(20;-30;50\right)\)
Câu 3:
Giải:
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\frac{a}{3b}=\frac{b}{3c}=\frac{c}{3d}=\frac{d}{3a}=\frac{a+b+c+d}{3b+3c+3d+3a}=\frac{a+b+c+d}{3\left(a+b+c+d\right)}=\frac{1}{3}\)
\(\frac{a}{3b}=\frac{1}{3}\Rightarrow3a=3b\Rightarrow a=b\)
Tương tự ta có b = c, c = d, d = a
\(\Rightarrow a=b=c=d\)
\(\Rightarrowđpcm\)
3, áp dụng tính chất dãy tỉ số bằng nhau:
=>\(\frac{a}{3.b}\)=\(\frac{b}{3.c}\)=\(\frac{c}{3.d}\) =\(\frac{d}{3.a}\) =\(\frac{a+b+c+d}{3\left(b+c+a+d\right)}\) =\(\frac{1}{3}\)
\(\Rightarrow\)\(\frac{a}{3b}\)=\(\frac{1}{3}\) =>\(\frac{1.b}{3.b}\) =\(\frac{b}{3.b}\) =>\(\frac{a}{3b}\) =\(\frac{b}{3b}\) =>...a=b (1)
\(\frac{c}{3d}\)=\(\frac{1}{3}\) =>\(\frac{1.d}{3.d}\) =\(\frac{d}{3d}\) =>\(\frac{c}{3d}\) =\(\frac{d}{3d}\) =>...c=d (2)
\(\frac{b}{3c}\) =\(\frac{1}{3}\) =>\(\frac{1.c}{3.c}\) =\(\frac{c}{3c}\)=>\(\frac{b}{3c}\) =\(\frac{c}{3c}\)=>..b=c (3)
\(\frac{d}{3a}\)=\(\frac{1}{3}\) =>\(\frac{1.a}{3.a}\) =\(\frac{a}{3a}\)=>\(\frac{d}{3a}\) =\(\frac{a}{3a}\)...=>d=a (4)
từ (1).(2).(3)(4)=>a=b=c=d(dpcm)
Xét tam giác ABC
Có: A+B+C=180
Hay:\(100^0+B+C=180^0\)
Vậy: \(B+C=80^0\)
\(B=\left(80+20\right):2=50^0\)
\(C=50^0-20^0=30^0\)