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 ?
142°
128°
52°
38°
I disagree with the answer. It is difficult because you do not see the figure. But the EXTERIOR angle (38 degrees) is adjacent to and interior angle at VERTEX H. To get the measurement of the interior angle we subtract 180-38=142 So, that interior ANGLE is 142 degrees, leaving the other 2 angles to measure to whatever is left from interior angle -142- to get to 180 degrees. So,180-142 is 38 degrees. That means that both vertex J and I, would have angles that together, measure 38 degrees, in order to have a triangle that has 180 degrees angles in total.
Since the line extending from vertex H forms an exterior angle of 38 degrees, the sum of the measures of the interior angles at vertex I and vertex J is equal to the sum of the exterior angle and the opposite interior angle.
In this case, the opposite interior angle is 180 - 38 = 142 degrees.
Therefore, the sum of the measures of the interior angles at vertex I and vertex J is 38 + 142 = 180 degrees.
So, the correct answer is 180 degrees, which is not listed among the given options.
To determine the sum of the measures of the interior angles at vertex I and vertex J, we need to first find the measure of the interior angle at vertex J.
Since the line extending outward from vertex H forms an exterior angle of 38 degrees, we can determine the measure of the interior angle at vertex J by subtracting this exterior angle from 180 degrees.
180° - 38° = 142°
Therefore, the measure of the interior angle at vertex J is 142 degrees.
Now, to find the sum of the measures of the interior angles at vertex I and vertex J, we simply add the measures of these two angles.
142° + 90° = 232°
The sum of the measures of the interior angles at vertex I and vertex J is 232 degrees.
So, the correct answer is: 232°
To find the sum of the measures of the interior angles at vertex I and vertex J, we need to use the following properties of triangles:
1. The sum of the measures of the interior angles of a triangle is 180 degrees.
2. The sum of the measures of an interior angle and its corresponding exterior angle is always 180 degrees.
In the given illustration, we are told that the line extending outward from vertex H forms an exterior angle of 38 degrees. Since the exterior angle is formed by extending a side of the triangle, we can say that the interior angle at vertex H is the supplement of the exterior angle, which is 180 - 38 = 142 degrees.
Now, let's look at the angles at vertex I and vertex J. Since these are interior angles, we know that the sum of their measures must be equal to the remaining interior angle at vertex H. Since the angle at vertex H is 142 degrees, the sum of the measures of the interior angles at vertex I and vertex J is also 142 degrees.
Therefore, the correct answer is 142°.