In any triangle, the exterior angle is equal to the sum of the two opposite interior angles. In this case, the exterior angle (at angle a) is given as 142 degrees. Using this property, we can express the relationship as follows:
\[ \text{Exterior angle} = \text{Angle a} + \text{Angle b} \]
So we have:
\[ 142° = a + b \]
Since the sum of the angles in a right triangle is always 180 degrees, and given that the right angle is 90 degrees, we can express the relationship between angle a and angle b as:
\[ a + b = 90° \]
Now we have two equations:
- \( a + b = 90° \)
- \( a + b = 142° \)
From the second equation, if we substitute \( b \) from the first equation into the second one:
\[ a + (90° - a) = 142° \] \[ 90° = 142° (which does not provide a solution using both angles)
Instead, since it is contradictory, we should look for \( b \) as the supplementary angle:
Therefore,
[ b = 142° - a \]
Since \( a + b = 90° \), we have \( b = 90° - a \), which helps us find that:
To find angle b:
- Since we established \( a + b = 90° \) to be supplemented by 142°:
Then, we rearrange:
- \( b = 142° - a \)
- \( a = 90° - b \)
To find \( b \):
\[ b + a = 90° b + (142° - b) = 90° 142° = 90° \] which leads \( b = 52° \)
Thus, the value of angle \( b \) is:
52°.