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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

38°
38 degrees

128°
128 degrees

142°
142 degrees

52°
52 degrees
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Answer 1

To find the sum of the measures of the interior angles at vertices I and J in triangle HIJ, we can use the relationship between the exterior angle and the interior angles of a triangle.

According to the exterior angle theorem, the exterior angle (which is 38 degrees in this case) is equal to the sum of the two non-adjacent interior angles. Therefore, the relationship can be represented as:

Exterior angle = Interior angle at I + Interior angle at J

So, we can express this mathematically as follows:

38° = Angle I + Angle J

To find the sum of the measures of the interior angles at vertices I and J, we need to rearrange our equation:

Angle I + Angle J = 38°

The question asks for the sum of the measures of the interior angles at vertices I and J.

Therefore, the correct answer is:

38°