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!