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 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.
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 obtuse triangle.
The third angle measure is 112°, and the triangle is an obtuse triangle.
The third angle measure is 112°, and the triangle is an obtuse triangle.
To find the measure of the third angle in the triangle, you can simply subtract the sum of the two given angles from 180 degrees.
In this case, the sum of the two given angles (22° + 46°) equals 68 degrees. Subtracting this from 180 degrees, we get:
180° - 68° = 112°
Therefore, the measure of the third angle is 112 degrees.
Now, to determine the type of triangle based on the angle measures, we can use the following definitions:
- An acute triangle has all three angles less than 90 degrees.
- A right triangle has one angle equal to 90 degrees.
- An obtuse triangle has one angle greater than 90 degrees.
Since all three angles of the triangle in question are less than 90 degrees (22°, 46°, and 112°), we can conclude that it is an acute triangle.
So, the correct response is:
"The third angle measure is 112°, and the triangle is an acute triangle."