In a triangle, the sum of all interior angles is always 180 degrees. Given that the exterior angle at vertex H is 38 degrees, we can use the exterior angle theorem. The exterior angle at vertex H is equal to the sum of the two opposite interior angles, which are the angles at vertices I and J.
Let the interior angles at vertices I and J be represented as \( \angle I \) and \( \angle J \).
According to the exterior angle theorem: \[ \text{Exterior angle} = \angle I + \angle J \] So, \[ 38^\circ = \angle I + \angle J \] To find the sum of the angles at vertices I and J, we can directly use the equation we have derived: \[ \angle I + \angle J = 38^\circ \] Thus, if we are looking for the sum of the measures of the interior angles at vertex I and vertex J, we find: \[ \text{Sum} = 38^\circ \]
So, the correct response is: 38°.