In any triangle, the exterior angle is equal to the sum of the two opposite interior angles. According to the information given, the exterior angle at angle \(a\) is \(142^\circ\).
Let angle \(b\) be represented as \(b\) and angle \(a\) remain \(a\). The relation can be set up as follows:
\[ \text{Exterior angle} = a + b \]
Substituting the exterior angle:
\[ 142^\circ = a + b \]
From the properties of a right triangle, we know that the sum of angles \(a\) and \(b\) must equal \(90^\circ\) because the right angle accounts for \(90^\circ\) of the total \(180^\circ\).
Thus:
\[ a + b = 90^\circ \]
Now we can substitute \(90^\circ - b\) for \(a\):
\[ 142^\circ = (90^\circ - b) + b \]
Solving for \(b\):
\[ 142^\circ = 90^\circ \]
From \(90^\circ + b = 142^\circ\):
\[ b = 142^\circ - 90^\circ = 52^\circ \]
Thus, the value of angle \(b\) is \(52^\circ\).
So the answer is:
52°
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