Question

Tính các góc hình thang ABCD ( \(AB\)// \(CD\)) biết \(\widehat{A}=3\widehat{D}\)và \(\widehat{B}-\widehat{C}=30^o\)

Answer 1

+) Vì AB // CD nên :

\(\widehat{A}+\widehat{D}=180^o\)( 2 góc trong cùng phía )

Có : \(\widehat{A}=3\widehat{D}\)

\(\Rightarrow3\widehat{D}+\widehat{D}=180^o\)

\(4\widehat{D}=180^o\)

\(\widehat{D}=\frac{180^o}{4}=45^o\)

\(\Rightarrow\widehat{A}=45^o\cdot3=135^o\)

+) Vì AB // CD ta có :

\(\widehat{B}+\widehat{C}=180^o\)( hai góc trong cùng phía )

Mà \(\widehat{B}-\widehat{C}=30^o\)

\(\Rightarrow\widehat{B}=\left(180+30\right)\div2=105^o\)

\(\Rightarrow\widehat{C}=105^o-30^o=75^o\)