The diagram you have uploaded shows a pair of intersecting lines with angles marked as $a^\circ$, $b^\circ$, and $c^\circ$. One of the angles is given as $25^\circ$. To work out the sizes of the lettered angles $a^\circ$, $b^\circ$, and $c^\circ$, let's follow the properties of angles on intersecting lines and parallel lines:

1. Angles on a straight line: Angles on a straight line add up to 180°. This will help us find $b$.
2. Vertically opposite angles: Vertically opposite angles are equal, which will help in finding $a$ and $c$.

Step-by-step Solution:

• Angle $b$: Angle $b$ is on a straight line with the given angle $25^\circ$. Therefore: $b = 180^\circ - 25^\circ = 155^\circ$

• Angle $a$: Angle $a$ is vertically opposite to the angle $25^\circ$, so: $a = 25^\circ$

• Angle $c$: Angle $c$ is vertically opposite to angle $b$, and since vertically opposite angles are equal: $c = 155^\circ$

Final Answer:

• $a = 25^\circ$
• $b = 155^\circ$
• $c = 155^\circ$

These values are based on the angle properties of intersecting lines.

Would you like more details on these angle rules, or do you have any other questions? Here are 5 relative questions that could help you expand your understanding:

1. What are alternate interior angles and how do they relate to parallel lines?
2. Can angles on parallel lines also be supplementary?
3. What other types of angles are formed when two lines intersect?
4. How can you determine if two lines are parallel using angle properties?
5. How do corresponding angles help in proving two lines are parallel?

Tip: Always check for vertically opposite angles when lines intersect—they are often equal and can simplify solving the problem!