a) Vì \(\hept{\begin{cases}a⊥d\\c⊥d\end{cases}}\Rightarrow a//c\)
\(\Rightarrow\widehat{A_1}=\widehat{C_1}\left(\text{2 góc đồng vị}\right)\) \(\Rightarrow\widehat{C_1}=50^o\)
b) Ta có : \(\widehat{A_1}+\widehat{A_2}=180^o\left(\text{ 2 góc kề bù}\right)\)\(\Rightarrow50^o+\widehat{A_2}=180^o\Rightarrow\widehat{A_2}=180^o-50^o=130^o=\widehat{B_1}\)
Mà \(\widehat{A_2}\text{ và }\widehat{B_1}\text{ là 2 góc so le trong}\)=> a // b mà a ⊥ d => b ⊥ d
c) Vẽ Bx là tia phân giác của \(\widehat{EBC}\Rightarrow\widehat{B_2}=\frac{\widehat{EBC}}{2}=\frac{130^o}{2}=65^o\)
∆MBC có :
\(\widehat{M_2}+\widehat{B_2}+\widehat{C_1}=180^o\left(\text{ tổng 3 góc của 1 tam giác}\right)\)
\(\Rightarrow\widehat{M_2}+65^o+50^o=180^o\Rightarrow\widehat{M_2}=65^o\)
Lại có \(\hept{\begin{cases}\widehat{F_1}+\widehat{E_2}=\widehat{EMC}\left(\text{ do }\widehat{EMC}\text{ là góc ngoài của }∆EFM\right)\\\widehat{EMC}=\widehat{M_1}+\widehat{M_2}\end{cases}}\)
\(\Rightarrow\widehat{F_1}+\widehat{E_2}=\widehat{M_1}+\widehat{M_2}\)\(\Rightarrow90^o+\widehat{E_2}=\widehat{M_1}+65^o\)
\(\Rightarrow\widehat{M_1}=\widehat{E_2}+25^o\)
Mà ∆EBM có :
\(\widehat{E_1}+\widehat{M_1}+\widehat{B_2}=180^o\left(\text{ tổng 3 góc của 1 tam giác}\right)\)
\(\Rightarrow\widehat{E_2}+\left(\widehat{E_2}+25^o\right)+65^o=180^o\)
\(\Rightarrow2.\widehat{E_2}+90^o=180^o\)\(\Rightarrow2.\widehat{E_2}=90^o\Rightarrow\widehat{E_2}=45^o\)
\(\Rightarrow\widehat{M_2}=\widehat{E_2}+25^o=45^o+25^o=70^o\)
