1. **Stating the problem:** We are given a geometry figure with intersecting lines and several angles labeled with values or expressions. We need to find the measures of angles $\angle 1$ through $\angle 7$. 2. **Given information:** - $m\angle 1 = 144^\circ$ (top-left region) - $m\angle 5 = 95^\circ$ (below the crossing) - Other angles near the intersection are labeled with numbers or expressions: 3, 2, 4, 3b. 3. **Key geometry rules:** - Vertical angles are equal. - Angles on a straight line sum to $180^\circ$. - Angles around a point sum to $360^\circ$. 4. **Find $m\angle 2$ and $m\angle 4$ using vertical angles:** Since $m\angle 1 = 144^\circ$, the vertical angle opposite it ($m\angle 3$) is also $144^\circ$. 5. **Find $m\angle 2$ and $m\angle 4$ using linear pairs:** Angles $\angle 1$ and $\angle 2$ are adjacent and form a straight line, so $$m\angle 1 + m\angle 2 = 180^\circ$$ $$144 + m\angle 2 = 180$$ $$m\angle 2 = 180 - 144 = 36^\circ$$ Similarly, $\angle 3$ and $\angle 4$ form a straight line, so $$m\angle 3 + m\angle 4 = 180^\circ$$ $$144 + m\angle 4 = 180$$ $$m\angle 4 = 36^\circ$$ 6. **Find $m\angle 6$ and $m\angle 7$ using vertical angles and linear pairs:** Given $m\angle 5 = 95^\circ$, its vertical angle $m\angle 7$ is also $95^\circ$. Angles $\angle 5$ and $\angle 6$ form a straight line, so $$m\angle 5 + m\angle 6 = 180^\circ$$ $$95 + m\angle 6 = 180$$ $$m\angle 6 = 85^\circ$$ 7. **Summary of angle measures:** $$m\angle 1 = 144^\circ$$ $$m\angle 2 = 36^\circ$$ $$m\angle 3 = 144^\circ$$ $$m\angle 4 = 36^\circ$$ $$m\angle 5 = 95^\circ$$ $$m\angle 6 = 85^\circ$$ $$m\angle 7 = 95^\circ$$ These values satisfy the rules of vertical angles and linear pairs in the figure.