Đáp án:
`\hat{A}=50^o`
`\hat{B}=180^o`
`\hat{C}=30^o`
`\hat{D}=100^o`
Giải thích các bước giải:
Vì `\hat{B}+\hat{C}=210^o`
`\hat{B}+\hat{D}=280^o`
`=>\hat{B}+\hat{D}-(\hat{B}+\hat{C})=280^o-210^o`
`=>\hat{D}-\hat{C}=70^o`
mà `\hat{C}+\hat{D}=130^o`
`=>\hat{C}=(130^o-70^o):2=30^o(1)`
`=>\hat{D}=130^o-30^o=100^o(2)`
`=>\hat{B}=280^o-\hat{D}=180^o(3)`
Xét tứ giác `ABCD` có :
`\hat{A}+\hat{B}+\hat{C}+\hat{D}=360^o`
`=>\hat{A}+180^o +30^o +100^o=360^o`
`=>\hat{A}=50^o(4)`
Từ `(1)(2)(3)(4)=>dpcm`
