1. **Stating the problem:** We are given a zigzag line with 5 segments and several angles: 88°, 92°, 81°, and 64°. We need to find the measures of angles $m\angle 1$, $m\angle 2$, $m\angle 3$, $m\angle 4$, and $m\angle 5$. 2. **Understanding angle relationships:** Adjacent angles on a straight line sum to 180°. Angles around a point sum to 360°. We will use these facts to find unknown angles. 3. **Finding $m\angle 1$:** Given segment 1 forms an 88° angle with the horizontal line. Since the horizontal line and segment 1 form this angle, $m\angle 1 = 88^\circ$. 4. **Finding $m\angle 2$:** Segment 2 forms a 92° angle with the horizontal line. Since the horizontal line and segment 2 form this angle, $m\angle 2 = 92^\circ$. 5. **Finding $m\angle 3$ and $m\angle 4$:** Segments 3 and 4 form an 81° angle with each other. The angles around the vertex where segments 3 and 4 meet sum to 180° (straight line). So, $$m\angle 3 + m\angle 4 = 180^\circ$$ Given the angle between them is 81°, the other angle at that vertex is $$180^\circ - 81^\circ = 99^\circ$$ Assuming $m\angle 3 = 81^\circ$ and $m\angle 4 = 99^\circ$. 6. **Finding $m\angle 5$:** Segment 5 forms a 64° angle with the last segment (segment 4). Since these two segments form this angle, $m\angle 5 = 64^\circ$. **Final answers:** $$m\angle 1 = 88^\circ$$ $$m\angle 2 = 92^\circ$$ $$m\angle 3 = 81^\circ$$ $$m\angle 4 = 99^\circ$$ $$m\angle 5 = 64^\circ$$