1. **Problem Statement:** Given a graph with multiple intersecting lines and some known angle measures, find the unknown angles labeled m\angle9, m\angle10, m\angle12, m\angle13, m\angle17, m\angle18, m\angle19, m\angle20, m\angle21, m\angle22, m\angle23, m\angle24, m\angle25, m\angle26, m\angle27, m\angle28, m\angle29, m\angle30. 2. **Key Concepts:** - Vertical angles are equal. - Angles on a straight line sum to 180°. - Angles around a point sum to 360°. - Adjacent angles in a triangle sum to 180°. 3. **Step-by-step solution for m\angle9:** - From the graph, m\angle9 is vertically opposite to m\angle7. - Since vertical angles are equal, $$m\angle9 = m\angle7 = 114^\circ$$. 4. **Step-by-step solution for m\angle10:** - m\angle10 and m\angle8 are supplementary (on a straight line). - Given m\angle8 = 90°, so $$m\angle10 = 180^\circ - 90^\circ = 90^\circ$$. 5. **Step-by-step solution for m\angle12:** - m\angle12 is vertical to m\angle11. - Given m\angle11 = 64°, so $$m\angle12 = 64^\circ$$. 6. **Step-by-step solution for m\angle13:** - m\angle13 and m\angle14 are supplementary. - Given m\angle14 = 50°, so $$m\angle13 = 180^\circ - 50^\circ = 130^\circ$$. 7. **Step-by-step solution for m\angle17:** - m\angle17 is vertical to m\angle16. - Given m\angle16 = 50°, so $$m\angle17 = 50^\circ$$. 8. **Step-by-step solution for m\angle18:** - m\angle18 and m\angle15 are supplementary. - Given m\angle15 = 40°, so $$m\angle18 = 180^\circ - 40^\circ = 140^\circ$$. 9. **Step-by-step solution for m\angle19:** - m\angle19 is vertical to m\angle20. - m\angle20 is vertical to m\angle19, so they are equal. - To find m\angle19, use the triangle or linear pair relations from the graph (assuming m\angle19 + m\angle20 = 180°). - Since m\angle19 = m\angle20, $$2m\angle19 = 180^\circ \Rightarrow m\angle19 = 90^\circ$$. 10. **Step-by-step solution for m\angle20:** - From above, $$m\angle20 = 90^\circ$$. 11. **Step-by-step solution for m\angle21 to m\angle30:** - Using vertical angles and supplementary angles rules, and given values, we find: - m\angle21 = m\angle22 = 64° (vertical to m\angle33) - m\angle23 = m\angle24 = 116° (vertical to m\angle34) - m\angle25 = m\angle26 = 64° (vertical to m\angle5) - m\angle27 = m\angle28 = 116° (vertical to m\angle3) - m\angle29 = m\angle30 = 90° (vertical to m\angle31 and m\angle32) **Final answers:** $$m\angle9 = 114^\circ$$ $$m\angle10 = 90^\circ$$ $$m\angle12 = 64^\circ$$ $$m\angle13 = 130^\circ$$ $$m\angle17 = 50^\circ$$ $$m\angle18 = 140^\circ$$ $$m\angle19 = 90^\circ$$ $$m\angle20 = 90^\circ$$ $$m\angle21 = 64^\circ$$ $$m\angle22 = 64^\circ$$ $$m\angle23 = 116^\circ$$ $$m\angle24 = 116^\circ$$ $$m\angle25 = 64^\circ$$ $$m\angle26 = 64^\circ$$ $$m\angle27 = 116^\circ$$ $$m\angle28 = 116^\circ$$ $$m\angle29 = 90^\circ$$ $$m\angle30 = 90^\circ$$