Question

Tứ giác ABCD có Cˆ = 50⁰, Dˆ = 80⁰ , Aˆ - Bˆ = 20⁰ . Tính số đo các góc A và B

 

 

Answer 1

Vì tứ giác ABCD có:

 \(\widehat{A}+\widehat{B}+\widehat{C}+\widehat{D}=360^o\\ \Leftrightarrow\left(\widehat{A}+\widehat{B}\right)+50^o+80^o=360^o\\ \Leftrightarrow\widehat{A}+\widehat{B}=230^o\)

Mặt khác: \(\widehat{A}-\widehat{B}=20^o\Rightarrow\widehat{A}=20^o+\widehat{B}\)

\(\Rightarrow\widehat{B}+20^o+\widehat{B}=230^o\\ \Leftrightarrow2\widehat{B}+20^o=230^o\\ \Leftrightarrow2\widehat{B}=210^o\\ \Leftrightarrow\widehat{B}=210^o:2=105^o\\ \Rightarrow\widehat{A}=20^o+105^o=125^o\)

Answer 2

Tổng 4 góc trong tứ giác là 360^o 

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

⇒ \(\widehat{A}+\widehat{B}+\)50^o+80^o=360^o

⇒ \(\widehat{A}+\widehat{B}\)=230^o

\(\widehat{A}+\widehat{B}\)=230^o, \(\widehat{A}-\widehat{B}\)=20^o⇒\(\widehat{A}+\widehat{B}+\widehat{A}-\widehat{B}\)=250^o

                                                ⇒ \(2\widehat{A}\)=250^o

                                        ⇒ \(\widehat{A}\)=125^o

\(\widehat{A}+\widehat{B}\)=230^o

⇒ 125^o+\(\widehat{B}\)=230^o

⇒\(\widehat{B}\)=105^o