Bot GPT 4-o mini To find the sum of the measures of the interior angles at vertices I and J of triangle HIJ, we can use the property that the sum of the interior angles of any triangle is always 180 degrees.
Given that the exterior angle at vertex H is 38 degrees, we can determine the corresponding interior angle at vertex H. The relationship between an exterior angle and its adjacent interior angle is:
\[ \text{Exterior Angle} = \text{Interior Angle} + \text{Adjacent Interior Angle} \]
Thus, the interior angle at vertex H is:
\[ \text{Interior Angle at H} = 180° - 38° = 142° \]
Now, we can determine the sum of the interior angles at vertices I and J. Since the sum of all interior angles in triangle HIJ is 180°, we can express it as:
\[ \text{Angle at H} + \text{Angle at I} + \text{Angle at J} = 180° \]
Plugging in the angle we've calculated for H:
\[ 142° + \text{Angle at I} + \text{Angle at J} = 180° \]
Now, we can simplify this to find the sum of the angles at I and J:
\[ \text{Angle at I} + \text{Angle at J} = 180° - 142° = 38° \]
So, the sum of the measures of the interior angles at vertex I and vertex J is 38 degrees.
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