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. The third angle measure is 112° , and the triangle is an obtuse triangle.
2. The third angle measure is 112° , and the triangle is an acute triangle
3. The third angle measure is 128° , and the triangle is an obtuse triangle
4. The third angle measure is 68° , and the triangle is an obtuse triangle
To find the third angle measure, we can use the fact that the sum of the angles in a triangle is always 180°.
22° + 46° + x = 180°
68° + x = 180°
x = 112°
So, the third angle measure is 112°.
Regarding the type of triangle, an obtuse triangle has one angle that is greater than 90°. Since the third angle measure is 112°, which is greater than 90°, the triangle is an obtuse triangle.
Therefore, the correct option is:
1. The third angle measure is 112°, and the triangle is an obtuse triangle.
To find the measure of the third angle in a triangle, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
Given that one angle is 22 degrees and another angle is 46 degrees, we can subtract the sum of these two angles from 180 to find the measure of the third angle.
180 - (22 + 46) = 180 - 68 = 112
Therefore, the third angle measure is 112 degrees.
To determine the type of triangle based on its angle measures:
- An obtuse triangle has one angle greater than 90 degrees. Since the third angle measure is 112 degrees, which is greater than 90 degrees, option 1 can be ruled out.
- An acute triangle has all angles less than 90 degrees. Since the third angle measure is 112 degrees, which is greater than 90 degrees, option 2 can also be ruled out.
Therefore, the correct answer is option 3: The third angle measure is 128°, and the triangle is an obtuse triangle.
To find the measure of the third angle in a triangle, you need to know that the sum of the angles in a triangle is always 180 degrees.
In this case, you are given that one angle measures 22 degrees and another angle measures 46 degrees. So, to find the measure of the third angle, you can subtract the sum of these two angles from 180 degrees.
22° + 46° = 68°
180° - 68° = 112°
Therefore, the measure of the third angle is 112 degrees.
Now, to determine the type of triangle, you need to analyze the angle measures.
If all angles in a triangle are less than 90 degrees, it is an acute triangle.
If one angle in a triangle is greater than 90 degrees, it is an obtuse triangle.
In this case, the third angle measures 112 degrees, which is greater than 90 degrees. Therefore, the triangle is an obtuse triangle.
So, the correct answer is:
Option 3. The third angle measure is 128°, and the triangle is an obtuse triangle.