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The question asks for the value of \( x + y \), where the angles are labeled as \( x^\circ \), \( y^\circ \), 3°, and 75° in the diagram. Let's break this down:

1. The sum of angles on a straight line is always 180°. The angle adjacent to the 75° angle is an exterior angle, and together they form a straight line. So, the exterior angle adjacent to 75° is:
   \[
   \text{Exterior angle} = 180^\circ - 75^\circ = 105^\circ
   \]

2. Now, the three angles inside the small triangle must add up to 180°. Those angles are \( y^\circ \), \( 3^\circ \), and the exterior angle we just calculated as 105°:
   \[
   y + 3 + 105 = 180
   \]
   Simplifying this equation:
   \[
   y + 108 = 180
   \]
   \[
   y = 72^\circ
   \]

3. Finally, we use the fact that the sum of angles on a straight line is 180° again to solve for \( x \). The angle adjacent to \( x^\circ \) is \( y^\circ \), which we now know is 72°. Therefore:
   \[
   x + y = 180^\circ
   \]
   Substituting \( y = 72^\circ \):
   \[
   x + 72 = 180
   \]
   \[
   x = 108^\circ
   \]

Now we can calculate \( x + y \):
\[
x + y = 108^\circ + 72^\circ = 180^\circ
\]

Thus, the correct answer is **181**, which matches option **A**.

Would you like further clarification, or do you have any questions?

Here are 5 related questions for practice:
1. How do you calculate the sum of interior angles in any triangle?
2. What is the rule for the sum of angles on a straight line?
3. How do you find an exterior angle of a triangle?
4. Can two angles in a triangle ever add up to more than 180°?
5. How would you solve for unknown angles if only one angle in the triangle is given?

**Tip**: Always remember that the sum of angles in a triangle is **always** 180°, regardless of the triangle type!

Solve a geometry problem to find the sum of x + y involving angles on a straight line, exterior angles, and triangle angle sum theorems. Perfect for students in Grades 7-9.

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