If a triangle has a 22° angle and a 46° angle, what can be established about the third angle measure and the triangle? (1 point)
The third angle measure is 112° and the triangle is an obtuse triangle.
The thurd angle measure is 128° 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 68° and the triangle is an obtuse triangle
The third angle measure is 112° and the triangle is an acute triangle.
To find the measure of the third angle, subtract the sum of the given angles from 180° (since the sum of the angles in a triangle is always 180°).
So, the third angle measure would be 180° - (22° + 46°) = 112°.
Since the third angle measure is greater than 90° (acute angle), the triangle is an obtuse triangle.
Therefore, the correct answer is:
The third angle measure is 112° and the triangle is an obtuse triangle.
To determine the third angle measure of the triangle, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
So, the third angle measure can be found by subtracting the sum of the given angles (22° + 46°) from 180°:
Third angle measure = 180° - (22° + 46°)
Third angle measure = 180° - 68°
Third angle measure = 112°
Therefore, the third angle measure is 112°.
Now, to determine the type of triangle, we need to compare the measures of the angles to the definitions of triangle types.
- An acute triangle has all three angles less than 90°.
- A right triangle has one angle equal to 90°.
- An obtuse triangle has one angle greater than 90°.
In this case, since the third angle measure is 112°, which is greater than 90°, the triangle is an obtuse triangle.
So, the correct answer is: The third angle measure is 112°, and the triangle is an obtuse triangle.