if a triangle has a 22 degree angle and a 46 degree angle, what can be established about the third angle measure and the type of triangle?
a. The third angle measure is 112 degrees, and the triangle is an acute triangle
b. The third angle measure is 128 degrees, and the triangle is an obtuse triangle
c. The third angle measure is 68 degrees, and the triangle is an obtuse triangle
d. The third angle measure is 112 degrees, 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.
Let x be the measure of the third angle. Therefore, we have the equation:
22 + 46 + x = 180 degrees
Simplifying the equation:
68 + x = 180 degrees
Subtracting 68 from both sides of the equation:
x = 112 degrees
Therefore, the third angle measure is 112 degrees.
To determine the type of triangle, we need to analyze the angle measures.
Since all three angles in the triangle are less than 90 degrees (22 degrees + 46 degrees + 112 degrees = 180 degrees), the triangle is an acute triangle.
So, the answer is:
a. The third angle measure is 112 degrees, and the triangle is an acute triangle.
To find the measure of the third angle in a triangle, we can use the fact that the sum of all three angles in a triangle is always 180 degrees.
In this case, we are given that one angle is 22 degrees and another angle is 46 degrees. To find the measure of the third angle, we can subtract the sum of the two given angles from 180 degrees.
Third angle measure = 180 degrees - (22 degrees + 46 degrees)
Third angle measure = 180 degrees - 68 degrees
Third angle measure = 112 degrees
So the third angle in the triangle measures 112 degrees.
To determine the type of triangle, we need to consider the measures of all three angles.
If all three angles in a triangle are less than 90 degrees, then the triangle is called an acute triangle.
If one angle in a triangle is greater than 90 degrees, then the triangle is called an obtuse triangle.
In this case, since the third angle in the triangle measures 112 degrees, which is greater than 90 degrees, the triangle is an obtuse triangle.
Therefore, the correct answer is option D: The third angle measure is 112 degrees, 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 interior angles of a triangle is always 180 degrees.
Let's denote the third angle as "x".
Given that one angle of the triangle is 22 degrees and the second angle is 46 degrees, we can set up the following equation:
22 + 46 + x = 180.
Simplifying the equation, we have:
68 + x = 180.
Subtracting 68 from both sides, we find:
x = 180 - 68.
Therefore, the measure of the third angle is 112 degrees.
Now let's determine the type of triangle based on the angle measures.
In an acute triangle, all three angles are less than 90 degrees.
In an obtuse triangle, exactly one angle is greater than 90 degrees.
Since the third angle measure is 112 degrees, which is greater than 90 degrees, the triangle is an obtuse triangle.
Therefore, the correct answer is option d. The third angle measure is 112 degrees, and the triangle is an obtuse triangle.