`#3107.\text{DN}`
`1.`
a.
Vì `\text {AB // CD}`
\(\Rightarrow\widehat{\text{A}}+\widehat{\text{D}}=180^0\\ \Rightarrow x+60^0=180^0\\ \Rightarrow x=120^0\)
Xét tứ giác ABCD:
\(\widehat{\text{A}}+\widehat{\text{B}}+\widehat{\text{C}}+\widehat{\text{D}}=360^0\\ \Rightarrow120^0+110^0+y+60^0=360^0\\ \Rightarrow y=70^0\)
Vậy, `x = 120^0; y = 70^0`
b.
Vì ABCD là hình thang
\(\Rightarrow\text{ AD // BC}\)
\(\Rightarrow\widehat{\text{A}}+\widehat{\text{B}}=180^0\left(\text{2 góc trong cùng phía bù nhau}\right)\)
\(\Rightarrow x+90^0=180^0\)
\(\Rightarrow x=90^0\)
Ta có:
\(\widehat{\text{D}_1}+\widehat{\text{D}_2}=180^0\left(\text{kề bù}\right)\)
\(\Rightarrow50^0+\widehat{\text{D}_2}=180^0\)
\(\Rightarrow\widehat{\text{D}_2}=130^0\)
Xét tứ giác ABCD:
\(\widehat{\text{A}}+\widehat{\text{B}}+\widehat{\text{C}}+\widehat{\text{D}_2}=360^0\\ \Rightarrow90^0+90^0+y+130^0=360^0\\ \Rightarrow y=50^0\)
Vậy, `x = 90^0; y = 50^0`
c.
Vì ABCD là hình thang
\(\Rightarrow\text{ AB // CD}\)
\(\Rightarrow\widehat{\text{A}}+\widehat{\text{D}}=180^0\left(\text{2 góc trong cùng phía bù nhau}\right)\)
\(\Rightarrow2y+y=180^0\)
\(\Rightarrow 3y=180^0\)
\(\Rightarrow y=60^0\)
Vậy, \(\widehat{\text{D}}=60^0\)
Mà \(\widehat{\text{A}}=2y\)
\(\Rightarrow\widehat{\text{A}}=2\cdot60=120^0\)
Vì `\text {AB // CD}`
\(\Rightarrow\widehat{\text{B}}+\widehat{\text{C}}=180^0\)
\(\Rightarrow3x+x=180^0\)
\(\Rightarrow4x=180^0\)
\(\Rightarrow x=45^0\)
Vậy, \(\widehat{\text{C}}=45^0\)
Mà \(\widehat{\text{B}}=3x\)
\(\Rightarrow\widehat{\text{B}}=3\cdot45^0=135^0\)
Vậy, số đo các góc trong hình thang ABCD lần lượt là \(\widehat{\text{A}}=120^0;\widehat{\text{B}}=135^0;\widehat{\text{C}}=45^0;\widehat{\text{D}}=60^0.\)
________
Xét tứ giác ABCD:
\(\widehat{\text{A}}+\widehat{\text{B}}+\widehat{\text{C}}+\widehat{\text{D}}=360^0\)
\(\Rightarrow90^0+40^0+x+90^0=360^0\)
\(\Rightarrow x=140^0\)
Vậy, số đo của \(\widehat{\text{C}}=140^0.\)
_________
Vì ABCD là hình thang
\(\Rightarrow\text{ AD // BC}\)
\(\Rightarrow\widehat{\text{A}}+\widehat{\text{B}}=180^0\left(\text{2 góc trong cùng phía bù nhau}\right)\)
\(\Rightarrow y+60^0=180^0\)
\(\Rightarrow y=120^0\)
Vì \(\widehat{\text{A}}=\widehat{\text{C}}\left(y=y\right)\)
\(\Rightarrow\widehat{\text{A}}=\widehat{\text{C}}=120^0\)
Xét tứ giác ABCD:
\(\widehat{\text{A}}+\widehat{\text{B}}+\widehat{\text{C}}+\widehat{\text{D}}=360^0\)
\(\Rightarrow120^0+60^0+120^0+x=360^0\)
\(\Rightarrow x=60^0\)
Vậy, số đo của \(\widehat{\text{D}}=60^0;\widehat{\text{A}}=\widehat{\text{C}}=120^0.\)
