Question

cho tam giac ABC co goc A=100

a)Tinh tong B+C

b)Ve cac tia pha giac cua B va C cat nhau tai diem M

Tinh so do goc BMC

Answer 1

a) Trong tam giác ABC có: \(\widehat{A}+\widehat{B}+\widehat{C}=180\Rightarrow100+\widehat{B}+\widehat{C}=180\Rightarrow\widehat{B}+\widehat{C}=80\)

b) Do: \(\widehat{ABC}+\widehat{ACB}=80\Rightarrow\frac{1}{2}\widehat{ABC}+\frac{1}{2}\widehat{ACB}=40\)

Mà: \(\widehat{MCB}=\frac{1}{2}\widehat{ACB};\widehat{MBC}=\frac{1}{2}\widehat{ABC}\)

\(\Rightarrow\widehat{MCB}+\widehat{MBC}=\frac{1}{2}\widehat{ACB}+\frac{1}{2}\widehat{ABC}\Rightarrow\widehat{MCB}+\widehat{MBC}=40\)

Mặt khác: Trong tam giác MBC có: \(\widehat{MBC}+\widehat{MCB}+\widehat{CMB}=180\Rightarrow40+\widehat{CMB}=180\Rightarrow\widehat{CMB}=140\)