To determine how many triangles can be formed when one angle is 95 degrees and another angle is obtuse, we first need to understand the properties of triangles and the characteristics of angles.
In any triangle, the sum of the interior angles must equal 180 degrees. An obtuse angle is defined as an angle that is greater than 90 degrees but less than 180 degrees.
Given one angle is 95 degrees, if we denote the second obtuse angle as ‘x’, then we can formulate the following equation:
95 + x + third angle = 180
Here, the third angle can be represented as:
third angle = 180 – 95 – x = 85 – x
For ‘x’ to be obtuse, it must satisfy the condition: 90 < x < 180. However, if 'x' is greater than 95 (since it is obtuse), then:
85 – x = 85 – (95 + ε) = -10 – ε (where ε is a small positive number), which results in a negative angle. This is not possible as angles cannot be negative.
Therefore, we conclude that it is impossible to create a triangle with one angle as 95 degrees and another angle as obtuse. Thus, the answer is:
Zero triangles can be formed.