1. **Problem Statement:** Two parallel lines are cut by a transversal, and one angle measures 33 degrees. We need to find the measures of angles 1 through 7. 2. **Key Concept:** When two parallel lines are cut by a transversal, corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary (sum to 180 degrees). 3. **Given:** One angle is 33 degrees. 4. **Step 1: Identify angle 1.** If angle 1 is the given 33 degrees, then: $$m1 = 33$$ 5. **Step 2: Find angle 2.** Angle 2 is adjacent to angle 1 and forms a linear pair, so: $$m2 + m1 = 180$$ $$m2 + 33 = 180$$ $$m2 = 180 - 33 = 147$$ 6. **Step 3: Find angle 3.** Angle 3 corresponds to angle 1 (corresponding angles are equal): $$m3 = m1 = 33$$ 7. **Step 4: Find angle 4.** Angle 4 is adjacent to angle 3, so: $$m4 + m3 = 180$$ $$m4 + 33 = 180$$ $$m4 = 147$$ 8. **Step 5: Find angle 5.** Angle 5 is alternate interior to angle 2, so: $$m5 = m2 = 147$$ 9. **Step 6: Find angle 6.** Angle 6 is adjacent to angle 5, so: $$m6 + m5 = 180$$ $$m6 + 147 = 180$$ $$m6 = 33$$ 10. **Step 7: Find angle 7.** Angle 7 corresponds to angle 6, so: $$m7 = m6 = 33$$ **Final answers:** $$m1 = 33, m2 = 147, m3 = 33, m4 = 147, m5 = 147, m6 = 33, m7 = 33$$