How many triangles can be made if one angle is 95° and another angle is obtuse?
none since the sum of all angles in a triangle cannot be more than 180. obtuse angle is 90 degrees more and less than 180.
let's say the obtuse angle is 90 and you have a given angle and 95+90 = 185
To determine the number of triangles that can be formed with one angle measuring 95° and another angle being obtuse, we need to understand the conditions for forming a triangle.
In a triangle, the sum of all three angles must be 180°. Given that one angle is 95° and another angle is obtuse (which means greater than 90°), the third angle must be acute (less than 90°) in order for the sum to be 180°.
Let's consider the possible values for the third angle:
1. If the third angle is less than 90°, the sum of the angles will be less than 180°, and a triangle cannot be formed.
2. If the third angle is 90°, the sum of the angles will be 95° + 90° + 90° = 275°, which is greater than 180°, and a triangle cannot be formed.
3. If the third angle is between 90° and 85° (inclusive), the sum of the angles will still be greater than 180°, and a triangle cannot be formed.
Therefore, no triangles can be formed with one angle measuring 95° and another angle being obtuse.
To determine the number of triangles that can be made with one angle measuring 95° and another angle being obtuse, we need to consider the properties of triangles.
In a triangle, the sum of the interior angles is always 180°. Given that one angle is already fixed at 95°, the other two angles must add up to 180 - 95 = 85°.
For a triangle to exist, the sum of any two angles must be greater than the third angle. In this case, since one angle is already 95°, the other two angles must sum up to be greater than 85°.
Since one angle has already been fixed at 95°, there are only two possibilities for the obtuse angle:
1. If the obtuse angle is greater than 85°, the remaining angle must be less than (180 - 95) = 85°. For example, if the obtuse angle is 100°, the remaining angle can be (180 - 95 - 100) = -15°, which is not a valid angle measure. Thus, no triangle can be formed in this case.
2. If the obtuse angle is less than 85°, the remaining angle must be greater than (180 - 95) = 85°. For example, if the obtuse angle is 80°, the remaining angle can be (180 - 95 - 80) = 5°. In this case, a triangle can be formed.
Therefore, there is only one possible triangle that can be formed if one angle is 95° and another angle is obtuse.