Đáp án:
Bài 4: \(\widehat{D_{1}}=70°; \widehat{D_{2}}=110°\)
Bài 5: \(\widehat{D_{2}}=105°\); \(\widehat{C_{2}}=75°\)
Bài 6:
a.\(\widehat{A_{1}}=145°\)
b. Bằng nhau
Giải thích các bước giải:
Bài 4:
Theo đề: \(\widehat{C_{1}}-\widehat{C_{2}}=40°\)
\(\Leftrightarrow \widehat{C_{1}}=\widehat{C_{2}}+40°\)
Ta có: \(\widehat{C_{1}}+\widehat{C_{2}}=180°\)
\(\Leftrightarrow \widehat{C_{2}}+\widehat{C_{2}}+40°=180°\)
\(\Leftrightarrow 2\widehat{C_{2}}=140°\)
\(\Rightarrow \widehat{C_{2}}=70°\)
\(\Rightarrow \widehat{C_{1}}=70°+40°=110°\)
Do \(a//b\) nên
\(\widehat{C_{2}}=\widehat{D_{1}}=70°\) (so le trong)
\(\widehat{C_{1}}=\widehat{D_{2}}=110°\)
Bài 5:
Do \(a//b\) nên \(\widehat{C_{1}}=\widehat{D_{2}}\) (so le trong)
Theo đề: \(\widehat{C_{1}}-\widehat{D_{1}}=30°\)
\(\Leftrightarrow \widehat{D_{2}}-\widehat{D_{1}}=30°\)
\(\Leftrightarrow \widehat{D_{2}}=30°+\widehat{D_{1}}\)
Mà \(\widehat{D_{1}}+\widehat{D_{2}}=180°\)
\(\Leftrightarrow \widehat{D_{1}}+\widehat{D_{1}}+30°=180°\)
\(\Leftrightarrow 2.\widehat{D_{1}}=150°\)
\(\Rightarrow \widehat{D_{1}}=75°\)
\(\Rightarrow \widehat{D_{2}}=30°+75°=105°\)
\(\widehat{C_{2}}=\widehat{D_{1}}=75°\) (so le trong)
Bài 6:
a. Ta có: \(\widehat{A_{1}}=\widehat{A_{3}}\) (đối đỉnh)
\( \widehat{A_{1}}+\widehat{A_{2}}=180°\)
\(\widehat{A_{2}}=180°-\widehat{A_{1}}\)
Theo đề: \(\widehat{A_{1}}+\widehat{A_{2}}+\widehat{A_{3}}=325°\)
\(\Leftrightarrow \widehat{A_{1}}+180°-\widehat{A_{1}}+\widehat{A_{1}}=325°\)
\(\Leftrightarrow \widehat{A_{1}}=145°\)
b. Ta có: \(\widehat{A_{2}}=\widehat{B_{2}}\) (hai góc đồng vị)
Mà \(\widehat{B_{2}}=\widehat{B_{4}}\) (đối đỉnh)
\(\Rightarrow \widehat{A_{2}}=\widehat{A_{4}}\)
