To find the correct measure of angle \( b \), we need to understand the relationships between the angles provided.
Without a visual representation, it's difficult to specify the exact relationships. However, a common scenario could involve the angles being part of a triangle, a linear pair, or perhaps corresponding angles.
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If angles are part of a triangle: The sum of angles in a triangle is always \( 180^\circ \). If angle \( a \) measures \( 52^\circ \) and assuming angle \( b \) is another angle alongside it in the triangle, we can set up the equation: \[ a + b + c = 180^\circ \] where \( c \) is the remaining angle in the triangle. Without the value of \( c \) or a clear structure, we cannot directly solve for \( b \).
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If angles are supplementary: If angle \( b \) is part of a linear pair with another angle measuring \( a = 52^\circ \), then: \[ a + b = 180^\circ \] And solving for \( b \): \[ b = 180^\circ - 52^\circ = 128^\circ \] Based purely on this relationship, the student might have confused the angles or misidentified their relationship, leading to reporting \( 128^\circ \) incorrectly as \( m \angle b \).
Given the student reported \( m \angle b = 128^\circ \), it suggests he might have mistakenly thought angle \( a \) was different or that he calculated or represented the angles incorrectly.
Conclusion: The likely mistake is a misunderstanding of how to apply the angle relationships, such as not correctly identifying that the sum of angles needs to be utilized properly and therefore misjudging \( b \).
If you have more specific details or a diagram, we could provide a more precise answer!