Question

Tứ giác ABCD có \(\widehat{C}=60^{\sigma},\widehat{D}=80^{\sigma},\widehat{A}-\widehat{B}=10^{\sigma}\).Tính số đo của\(\widehat{A}\) và \(\widehat{B}\).

Answer 1

Ta có :

\(\widehat{A}+\widehat{B}+\widehat{C}+\widehat{D}=360^o\)

\(\Rightarrow\widehat{A}+\widehat{B}=360^o-\left(\widehat{C}+\widehat{D}\right)\)

\(\Rightarrow\widehat{A}+\widehat{B}=360^o-\left(60+80\right)=220^o\)

mà \(\widehat{A}-\widehat{B}=10^o\)

\(\Rightarrow\widehat{A}=\left(220-10\right):2=105^o\)

\(\Rightarrow\widehat{B}=105-10=95^o\)

Vậy \(\left\{{}\begin{matrix}\widehat{A}=105^o\\\widehat{B}=95^o\end{matrix}\right.\)