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Question
If a triangle has a 22° angle and a 46° angle, what can be established about the third angle measure and the type of triangle?(1 point)
Responses
The third angle measure is 112°, and the triangle is an obtuse triangle.
The third angle measure is 112 degrees , and the triangle is an obtuse triangle.
The third angle measure is 68°, and the triangle is an obtuse triangle.
The third angle measure is 68 degrees , and the triangle is an obtuse triangle.
The third angle measure is 112°, and the triangle is an acute triangle.
The third angle measure is 112 degrees , and the triangle is an acute triangle.
The third angle measure is 128°, and the triangle is an obtuse triangle.
The third angle measure is 128 degrees , and the triangle is an obtuse triangle.
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Answers: 1. The third angle measure is 112°, and the triangle is an obtuse triangle. 2. No, because there needs to be a third angle. 3. acute triangle 4. 52° 5. 38°
The correct response is: The third angle measure is 112°, and the triangle is an obtuse triangle.
To find the third angle measure of a triangle, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
Given that one angle of the triangle is 22 degrees and another angle is 46 degrees, we can add these two angles together:
22 + 46 = 68 degrees
So, the third angle measure is 68 degrees.
Now, to determine the type of triangle, we can analyze the angle measures.
If all three angles of a triangle are less than 90 degrees, then it is an acute triangle.
If one angle is greater than 90 degrees, then it is an obtuse triangle.
In this case, since the third angle measure is 68 degrees and less than 90 degrees, the triangle is an acute triangle.
Therefore, the correct response is:
"The third angle measure is 68 degrees, and the triangle is an acute triangle."
To find the measure of the third angle in a triangle, you need to subtract the sum of the two given angles from 180 degrees. In this case, the third angle measure would be 180 - (22 + 46) = 112 degrees.
Since the third angle measure is 112 degrees, we can establish that the triangle is an obtuse triangle.