Angles of Triangles Quick Check
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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
38°
38 degrees
52°
52 degrees
142°
142 degrees
128°
128 degrees
To find the sum of the measures of the interior angles at vertex I and vertex J, we need to determine the measure of the exterior angle at vertex H.
Since the exterior angle at vertex H is 38 degrees, we know that the sum of the measures of the exterior angle and the interior angle at a vertex is always 180 degrees.
Therefore, the measure of the interior angle at vertex H is 180 - 38 = 142 degrees.
Since the sum of the measures of the interior angles of a triangle is always 180 degrees, the sum of the measures of the interior angles at vertex I and vertex J is:
180 - measure of interior angle at vertex H = 180 - 142 = 38 degrees.
Therefore, the correct answer is 38 degrees.