Question

Use the image to answer the question.

An illustration shows triangle uppercase H uppercase I uppercase J. Uppercase H is the left vertex, uppercase I is the top vertex, and uppercase J is the right vertex. A line extending outward from uppercase H forms an exterior angle of 38 degrees.

What is the sum of the measures of the interior angles at vertex I
and vertex J
?

(1 point)
Responses

142°
142 degrees

38°
38 degrees

52°
52 degrees

128°
128 degrees
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Answer 1

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°.