To find the sum of the measures of the interior angles at vertices I and J in triangle HIJ, we can use the exterior angle theorem.
The exterior angle at vertex H is given as 38 degrees. According to the exterior angle theorem, the measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles. In this case, the exterior angle at H is equal to the sum of the angles at vertices I and J.
Therefore:
\[ \angle H + \angle I + \angle J = 180° \text{ (sum of angles in a triangle)} \]
And since:
\[ \angle H = 38° \]
We can replace it in the equation:
\[ 38° + \angle I + \angle J = 180° \]
Subtracting 38° from both sides gives:
\[ \angle I + \angle J = 180° - 38° = 142° \]
Thus, the sum of the measures of the interior angles at vertex I and vertex J is 142 degrees.
The correct response is:
142°