1. **State the problem:** We are given two transversals intersecting parallel lines with various angles labeled. We focus on Transversal Line 1 (red) to find the measurements of angles 1, 2, 3, 4, 5, and 6. 2. **Given:** - Interior Angle 1 = 55° - Interior Angle 2 = 125° 3. **Recall angle relationships:** - Interior angles on the same side of the transversal are supplementary (sum to 180°). - Corresponding angles are equal. - Vertically opposite angles are equal. 4. **Find m<5:** Since m<5 corresponds to m<1 (corresponding angles), and m<1 = 55°, then $$m<5 = 55^\circ$$ 5. **Find m<3:** m<3 and m<1 are vertically opposite angles, so $$m<3 = 55^\circ$$ 6. **Find m<2:** m<2 and m<1 are supplementary interior angles on the same side of the transversal, so $$m<2 + m<1 = 180^\circ$$ $$m<2 + 55 = 180$$ $$m<2 = 180 - 55 = 125^\circ$$ 7. **Find m<6:** m<6 corresponds to m<2 (corresponding angles), so $$m<6 = 125^\circ$$ 8. **Find m<1:** Given as 55°. 9. **Find m<4:** m<4 and m<2 are vertically opposite angles, so $$m<4 = 125^\circ$$ 10. **List all corresponding angles on Transversal Line 1:** - m<1 = 55° - m<3 = 55° - m<5 = 55° - m<2 = 125° - m<4 = 125° - m<6 = 125° **Final answers:** - m<5 = 55° - m<3 = 55° - m<2 = 125° - m<6 = 125° - m<1 = 55° - m<4 = 125° **Note:** The problem also mentions Transversal Line 2 with exterior angle $(x+32.67)^6$ and interior angle $147.33^6$ which are supplementary. To find $x$: $$ (x + 32.67) + 147.33 = 180 $$ $$ x + 180 = 180 $$ $$ x = 0 $$ Thus, $x=0$.