1. **Stating the problem:** We are given a figure with angles labeled involving the Greek letter $\xi$ and numbers 44, 66, and angles $a$, $b$, and $c$ to find. 2. **Understanding the figure and angles:** - The angle labeled 44$\xi$ is formed by a diagonal line intersecting a horizontal line. - The angle labeled 66$\xi$ is formed by a diagonal line intersecting another horizontal line. - Angles $a$, $b$, and $c$ are formed at intersections involving these lines. - The figure shows perpendicular lines, so some angles are right angles (90 degrees). 3. **Using angle relationships:** - Since the line with angle 44$\xi$ is perpendicular to the horizontal line, the angle adjacent to 44$\xi$ is $90 - 44\xi = 46\xi$. - Similarly, the angle adjacent to 66$\xi$ on the horizontal line is $90 - 66\xi = 24\xi$. 4. **Finding $m\angle a$:** - $m\angle a$ is vertically opposite to the angle 44$\xi$, so $m\angle a = 44\xi$. 5. **Finding $m\angle b$:** - $m\angle b$ is adjacent to 66$\xi$ and forms a right angle with it, so $m\angle b = 90 - 66\xi = 24\xi$. 6. **Finding $m\angle c$:** - $m\angle c$ is the angle between the vertical line and the lower horizontal line, which is a right angle, so $m\angle c = 90\xi$. **Final answers:** $$ m\angle a = 44\xi $$ $$ m\angle b = 24\xi $$ $$ m\angle c = 90\xi $$