To find the sum of the measures of the interior angles at vertices I and J given that the exterior angle is 38 degrees, we can use the relationship between interior and exterior angles.
The interior angle is supplementary to the exterior angle, which means:
\[ \text{Interior angle} + \text{Exterior angle} = 180° \]
Since the exterior angle is 38°, the corresponding interior angle would be:
\[ \text{Interior angle} = 180° - 38° = 142° \]
If we have both vertex I and vertex J with the same exterior angle, the sum of the interior angles at both vertices would be:
\[ 142° + 142° = 284° \]
However, if only one vertex has been described, then the answer is simply 142° for one vertex.
Thus, the possible sums of the measures of the interior angles at vertices I and J is 142° each. If interpreted as needing to specify both vertices separately, the correct answer still simplifies to being 142° from either one of them as a singular vertex if they are to be considered in isolation.
Given the multiple-choice options, the response should be 142° for one interior angle, but if both are asked for together (implying needing more than one angle) you'd use:
- 284° would not be in relation to those listed dimensions but makes sense if both angles summed were articulated.
So the most straightforward answer from the given options for either vertex represented would be 142°.
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