Use the image to answer the question.

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

52°
52 degrees

142°
142 degrees

Answer 1

To find the sum of the measures of the interior angles at vertex I and vertex J in triangle HIJ, we can use the fact that the sum of the interior angles of a triangle is always 180 degrees.

Given that an exterior angle at vertex H measures 38 degrees, we can find the two remote interior angles at vertices I and J.

The relationship between an exterior angle and its adjacent interior angle can be used here:

Exterior angle (at H) = Interior angle at I + Interior angle at J.

So, we know:

38 degrees = Angle I + Angle J

Since the sum of all interior angles in triangle HIJ is 180 degrees:

Angle I + Angle J + Angle H = 180 degrees

Angle H can be found using the exterior angle definition: Angle H = 180 - Exterior angle = 180 - 38 = 142 degrees.

Now we can substitute:

Angle I + Angle J + 142 = 180 Angle I + Angle J = 180 - 142 Angle I + Angle J = 38 degrees.

Thus, the sum of the measures of the interior angles at vertex I and vertex J is 38 degrees.

The correct response is: 38°