a) AB//CD \(\Rightarrow\widehat{B}+\widehat{C}=180^o\) (trong cùng phía)
\(\Rightarrow140^o+x=180^o\Rightarrow x=180^o-140^o=40^o\)
b) MN//PQ \(\Rightarrow\left\{{}\begin{matrix}\widehat{Q}+\widehat{M}=180^o\\\widehat{N}+\widehat{P}=180^o\end{matrix}\right.\) (trong cùng phía
\(\widehat{Q}+\widehat{M}=180^o\Rightarrow60^o+x=180^o\Rightarrow x=120^o\)
\(\widehat{N}+\widehat{P}=180^o\Rightarrow\left(180^o-\widehat{N_n}\right)+\widehat{P}=180^o\\ \Rightarrow\left(180^o-70^o\right)+y=180^o\Rightarrow110^o+y=180^o\\ \Rightarrow y=70^o\)
c) HG//KI \(\widehat{H}+\widehat{I}=180^o\) (trong cùng phía)
\(\Rightarrow x+4x=180^o\Rightarrow5x=180^o\Rightarrow x=\dfrac{180^o}{5}=36^o\)
d) Xét tứ giác STUV có:
\(\widehat{V}+\widehat{U}+\widehat{S}+\widehat{T}=360^o\\ \Rightarrow2x+x+90^o+90^o=360^o\\ \Rightarrow3x+180^o=360^o\Rightarrow3x=180^o\Rightarrow x=60^o\)
a) Vì AB//CD
\(\Rightarrow\widehat{ABC}+\widehat{BCD}=180^o\)
\(\Rightarrow140^o+x=180^o\)
\(\Rightarrow x=40^o\)
b) Vì MN//PQ
\(\Rightarrow\widehat{PQM}+\widehat{QMN}=180^o\)
\(\Rightarrow60^o+x=180^o\)
\(\Rightarrow x=120^o\)
Vì MN//PQ
\(\Rightarrow\widehat{QPN}\) bằng góc ngoài tại đỉnh N của tứ giác MNPQ (SLT)
\(\Rightarrow y=70^o\)
c) Vì HG//KI
\(\Rightarrow\widehat{GHI}+\widehat{HIK}=180^o\)
\(\Rightarrow4x+x=180^o\)
\(\Rightarrow5x=180^o\)
\(\Rightarrow x=36^o\)
d) Vì \(\left\{{}\begin{matrix}VS\perp ST\\UT\perp ST\end{matrix}\right.\rightarrow\) VS//UT
\(\Rightarrow\widehat{UVS}+\widehat{VUT}=180^o\)
\(\Rightarrow2x+x=180^o\)
\(\Rightarrow3x=180^o\)
\(\Rightarrow x=60^o\)
