If a triangle has a 22º angle and a 46º angle, what can be established about the third angle measure and the type of triangle?
The sum of the angles in a triangle is always 180º. Therefore, if a triangle has a 22º angle and a 46º angle, the measure of the third angle can be found by subtracting the sum of the given angles from 180º.
Third angle = 180º - (22º + 46º)
Third angle = 180º - 68º
Third angle = 112º
Therefore, the measure of the third angle is 112º.
Regarding the type of triangle, since none of the angles are equal, it is not an equilateral triangle. Additionally, since none of the angles are right angles (90º), it is not a right triangle either. Therefore, the triangle must be a scalene triangle.
Is the triangle obtuse or acute?
To determine if the triangle is obtuse or acute, we need to compare the measure of the third angle (112º) to 90º.
If the third angle is greater than 90º, the triangle is obtuse.
If the third angle is less than 90º, the triangle is acute.
In this case, the third angle (112º) is greater than 90º, so the triangle is obtuse.
To find the measure of the third angle and determine the type of triangle, we can use the fact that the sum of the angles in any triangle is always 180 degrees.
First, we add the given angles: 22º + 46º = 68º.
To find the measure of the third angle, we subtract the sum of the given angles from 180º: 180º - 68º = 112º.
So, the measure of the third angle is 112º.
Now, let's determine the type of triangle based on the angle measures:
- If all three angles of a triangle are less than 90 degrees, it is an acute triangle.
- If one angle of a triangle is exactly 90 degrees, it is a right triangle.
- If one angle of a triangle is greater than 90 degrees, it is an obtuse triangle.
In our case, none of the angles are exactly 90 degrees, so the triangle is not a right triangle.
Since all three angles (22º, 46º, and 112º) are less than 90 degrees, the triangle is an acute triangle.