To find angle \( b \) using the properties of exterior angles in triangles, we can use the fact that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles.
In this case, if angle \( a \) is an exterior angle of a triangle and measures \( 142^\circ \), then it can be expressed as:
\[ a = b + c \]
where \( b \) and \( c \) are the two interior angles opposite to the exterior angle \( a \).
Since we are not given the value of \( c \), we can only express \( b \) in terms of \( c \):
\[ b = a - c \]
Given that the value of \( a \) is \( 142^\circ \), one possible approach is to consider potential values for \( b \) based on common angle measures.
However, without additional information about \( c \) or the triangle itself, we cannot determine a specific numerical value for angle \( b \).
Let’s check if any of the provided options could logically fit this scenario:
- If \( b \) is \( 38^\circ \), that means \( c \) would be \( 104^\circ \) (since \( 142 - 38 = 104\)).
- If \( b \) is \( 92^\circ \), then \( c \) would be \( 50^\circ\) (since \( 142 - 92 = 50\)).
- The rest of the angle options yield similar results.
If we assume \( 142^\circ \) is indeed the declared exterior angle and derive possible \( c \) angles for each \(b\), we can inspect which of the options provided logically aligns with the rules of triangles (that the sum of interior angles is \( 180^\circ \)).
Nonetheless, please check the context of the triangle in the image you mentioned, as the specific answer might rely on that visual context. If you can, please provide additional information or context. Otherwise, without extra context, the option that fits typical angle relationships given \(142^\circ\) would likely be:
\[ b = 38^\circ \]
Final answer: 38 degrees.
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