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

52°
52 degrees

38°
38 degrees

128°
128 degrees

142°
142 degrees
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Answer 1

the correct anser is actually 38 degress.

Answer 2

In any triangle, the sum of the interior angles is always 180 degrees. Given that an exterior angle at vertex H measures 38 degrees, we can use the relationship between an exterior angle and the sum of the two opposite interior angles.

Specifically, the exterior angle is equal to the sum of the two non-adjacent interior angles:

\[
\text{Exterior Angle} = \text{Interior Angle at I} + \text{Interior Angle at J}
\]

Thus, we have:

\[
38 = \text{Interior Angle at I} + \text{Interior Angle at J}
\]

To find the sum of the measures of the interior angles at vertex I and vertex J, we set this equation:

\[
\text{Interior Angle at I} + \text{Interior Angle at J} = 38
\]

The two interior angles at I and J together equal 180 degrees minus the angle at H. Since we already know that the sum of the angles in triangle HIJ is 180 degrees:

\[
\text{Interior Angle at H} + \text{Interior Angle at I} + \text{Interior Angle at J} = 180
\]

Substituting the exterior angle:

\[
38 + \text{Interior Angle at I} + \text{Interior Angle at J} = 180
\]

This gives:

\[
\text{Interior Angle at I} + \text{Interior Angle at J} = 180 - 38 = 142
\]

Thus, the sum of the measures of the interior angles at vertex I and vertex J is **142 degrees**. The correct answer is:

**142°**