1. **Problem statement:** Given angle $xOy = 50^\circ$, draw angle $yOz$ supplementary to $xOy$. Check the truth of the following statements: 2. **Recall:** Supplementary angles sum to $180^\circ$. So, $$m(yOz) = 180^\circ - m(xOy) = 180^\circ - 50^\circ = 130^\circ.$$ 3. **Check statement a):** $m(yOz) = 130^\circ$ is correct because supplementary angles add to $180^\circ$. 4. **Check statement b):** Ot is the opposite ray of Ox, so $m(xOt) = 180^\circ$. Since $y$ lies between $x$ and $z$, and $m(xOy) = 50^\circ$, then $m(yOt) = m(xOt) - m(xOy) = 180^\circ - 50^\circ = 130^\circ$, not $50^\circ$. So statement b) is false. 5. **Check statement c):** Om bisects $xOy$, so $$m(xOm) = m(mOy) = \frac{50^\circ}{2} = 25^\circ.$$ On bisects $yOz$, so $$m(yOn) = m(nOz) = \frac{130^\circ}{2} = 65^\circ.$$ Then, $$m(OmOn) = m(mOy) + m(yOn) = 25^\circ + 65^\circ = 90^\circ.$$ So statement c) is true. 6. **Check statement d):** Oa is opposite ray of Oy, Ob is opposite ray of Ox. Then $xOy$ and $aOb$ share vertex O and their sides are opposite rays, so they are vertical angles (đối đỉnh). Statement d) is true. **Final answers:** a) True b) False c) True d) True