To determine how many triangles can be formed with one angle measuring 95 degrees and another angle being obtuse, let’s start by breaking down the properties of angles in a triangle.
In any triangle, the sum of the interior angles must always equal 180 degrees. This means that if you already have one angle of 95 degrees, the remaining two angles must sum to:
- 180 degrees – 95 degrees = 85 degrees
Now, let’s consider the second angle, which is stated to be obtuse. An obtuse angle is defined as an angle that measures greater than 90 degrees but less than 180 degrees. Therefore, since one angle is already 95 degrees, we can evaluate the possibilities for the second obtuse angle:
- Since the second angle must be obtuse (greater than 90 degrees), it must be more than 90 degrees.
- However, if the second angle were to be 90 degrees or more, we would have:
- Let’s say the second angle is denoted as ‘B’. If B is obtuse, this means B > 90.
- Given our earlier calculation, we found that the two remaining angles must together be 85 degrees. This condition cannot be satisfied because if B is more than 90 degrees (say, 91 degrees), the sum will exceed 95 degrees, thus violating the rule of angles in a triangle.
Thus, implementing both conditions leads to a critical realization: it’s impossible to have two angles in a triangle that both satisfy these conditions. Therefore, we can conclude that:
The answer is: 0 triangles can be formed.
In summary, if one angle is 95 degrees, then the other angle cannot be obtuse if we want to maintain the validity of the triangle’s angle sum property. Hence, there are no valid triangles that can be created under these parameters.