Ta có: \(\hat{mOx^{\prime}}+\hat{mOt^{\prime}}+\hat{mOy^{\prime}}=\hat{mOx^{\prime}}+\hat{mOx^{\prime}}+\hat{x^{\prime}Ot^{\prime}}+\hat{mOx^{\prime}}+\hat{x^{\prime}Oy^{\prime}}\)
\(=3\cdot\hat{mOx^{\prime}}+\hat{x^{\prime}Ot^{\prime}}+\hat{x^{\prime}Ot^{\prime}}+\hat{y^{\prime}Ot^{\prime}}\)
\(=3\cdot\hat{x^{\prime}Om}+2\cdot\hat{x^{\prime}Ot^{\prime}}+\hat{y^{\prime}Ot^{\prime}}\)
Op là phân giác của góc xOy
=>\(\hat{xOp}=\hat{yOp}=\frac12\cdot\hat{xOy}\)
\(\hat{tOp}=3\cdot\hat{qOp}\)
=>\(\hat{qOp}=\frac13\cdot\hat{tOp}=\frac13\cdot\left(\hat{xOp}-\hat{xOt}\right)=\frac13\left(\frac12\cdot\hat{xOy}-\hat{xOt}\right)\)
\(=\frac16\cdot\hat{xOy}-\frac13\cdot\hat{xOt}\)
Ta có: \(\frac{\hat{mOx^{\prime}}+\hat{mOt^{\prime}}+\hat{mOy^{\prime}}}{3}+\hat{mOq}\)
\(=\frac{3\cdot\hat{x^{\prime}Om}+2\cdot\hat{x^{\prime}Ot^{\prime}}+\hat{y^{\prime}Ot^{\prime}}}{3}+\hat{mOy}+\hat{yOp}+\hat{qOp}\)
\(=\frac{3\cdot\hat{x^{\prime}Om}+2\cdot\hat{x^{\prime}Ot^{\prime}}+\hat{y^{\prime}Ot^{\prime}}}{3}+\hat{mOy}+\frac12\cdot\hat{xOy}+\frac16\cdot\hat{xOy}-\frac13\cdot\hat{x^{\prime}Ot^{\prime}}\)
\(=\hat{x^{\prime}Om}+\frac23\cdot\hat{x^{\prime}Ot^{\prime}}+\frac13\cdot\hat{y^{\prime}Ot^{\prime}}+\hat{mOy}+\frac23\cdot\hat{xOy}-\frac13\cdot\hat{x^{\prime}Ot^{\prime}}\)
\(=\hat{x^{\prime}Oy}+\frac13\cdot\hat{x^{\prime}Ot^{\prime}}+\frac13\cdot\hat{y^{\prime}Ot^{\prime}}+\frac23\cdot\hat{xOy}=\hat{x^{\prime}Oy}+\frac13\cdot\hat{x^{\prime}Oy^{\prime}}+\frac23\cdot\hat{x^{\prime}Oy^{\prime}}\)
\(=\hat{x^{\prime}Oy}+\hat{x^{\prime}Oy^{\prime}}=180^0\)
