1. **Stating the problem:** We have three intersecting lines forming angles labeled $a\angle 5$, $44\angle 5$, $66\angle 5$, $c\angle 5$, and $b\angle 5$. We need to find the measures $m\angle a$, $m\angle b$, and $m\angle c$. 2. **Understanding the setup:** Two horizontal lines are parallel, and a vertical line intersects them, creating several angles. The angles on a straight line sum to $180^\circ$, and vertical angles are equal. 3. **Using angle relationships:** - Since $44^\circ$ and $a$ are adjacent on a straight line, $m\angle a + 44 = 180$. - Similarly, $66^\circ$ and $b$ are adjacent on a straight line, so $m\angle b + 66 = 180$. - Angles $a$ and $c$ are corresponding angles formed by the transversal and parallel lines, so $m\angle a = m\angle c$. 4. **Calculating $m\angle a$:** $$m\angle a = 180 - 44 = 136$$ 5. **Calculating $m\angle b$:** $$m\angle b = 180 - 66 = 114$$ 6. **Calculating $m\angle c$:** Since $m\angle c = m\angle a$, $$m\angle c = 136$$ **Final answers:** $$m\angle a = 136$$ $$m\angle b = 114$$ $$m\angle c = 136$$