Đáp án:
$\\$
Có : `hat{xOm}=3/4 hat{xOz}`
`-> hat{xOz}=4/3 hat{xOm}`
Do `Om` nằm giữa `Oz` cà `Ox`
`-> hat{xOm} + hat{mOz}=hat{xOz}`
`-> hat{xOm}+hat{mOz}=4/3 hat{xOm}`
`-> hat{mOz}=4/3 hat{xOm}-hat{xOm}`
`-> hat{mOz}=1/3 hat{xOm}`
Có : `hat{xOn} + hat{yOn}=180^o` (2 góc kề bù)
`-> hat{yOn}=180^o - hat{xOn}`
Lại có : `Om⊥On`
`-> hat{mOz}+hat{zOn}=90^o`
`->hat{zOn}=90^o - hat{mOz}`
Có : `hat{xOm}+hat{mOz}+hat{zOn}=hat{xOn}`
`-> hat{xOm} + (hat{mOz}+hat{zOn})=hat{xOn}`
`-> hat{xOm}+90^o = hat{xOn}`
`-> hat{xOm}+90^o =180^o - hat{yOn}`
`-> hat{xOm}=180^o - hat{yOn}-90^o`
`-> hat{xOm}=90^o - hat{yOn}`
`-> 1/3 hat{xOm}=1/3 (90^o - hat{yOn})`
`-> hat{mOz} = 30^o - 1/3 hat{yOn}`
`-> 90^o - hat{mOz}=90^o -30^o + 1/3 hat{yOn}`
`-> hat{zOn} = 60^o + 1/3 hat{yOn}`
`-> hat{zOn}-1/3 hat{yOn}=60^o` (đpcm)
