To solve for angle \( b \) using the properties of exterior angles of triangles, we need to remember that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Assuming you have a triangle with angle \( b \) and it's paired with an exterior angle of 232°, the relationship would be:
\[ \text{Exterior Angle} = \text{Angle 1} + \text{Angle 2} \]
Given that the exterior angle is 232°, we can write:
\[ 232° = a° + b° \]
where \( a° \) represents the other interior angle. Since we don't know what \( a° \) is, we need to check possible values for angle \( b \) given the answer options you provided: 232°, 92°, 38°, and 52°.
Let's investigate each option. The crucial point here is that an exterior angle should not be equal to either of the interior angles, as both angles must sum to that angle, along with another unknown angle.
Let's analyze the angles with the understanding that the sum of angles in a triangle is \( 180° \).
If you take 92° as angle \( b \): \[ 232° = a° + 92° \] Then, \[ a° = 232° - 92° = 140° \] 140° is a possible triangle angle.
If you take 38° as angle \( b \): \[ 232° = a° + 38° \] Then, \[ a° = 232° - 38° = 194° \] 194° is not a valid triangle angle.
If you take 52° as angle \( b \): \[ 232° = a° + 52° \] Then, \[ a° = 232° - 52° = 180° \] 180° also cannot be part of a triangle (must be less than 180°).
Finally, if you take 232° as angle \( b \), it violates the triangle property straight away because an angle in triangle cannot equal its exterior angle. Therefore, this wouldn't work.
From this analysis, the only valid angle for \( b \) is:
\[ \boxed{92°} \]
This conforms with the properties of triangles and ensures the angles relate correctly, while still adhering to the constraints of a triangle's angles.