Need help on the question below.
How many different triangles, if any, can be drawn with on 20 degree angle, one 45 degree angle, and one 155 degree angle.
Thanks....
none, the sum of your angles ≠ 180°
360
To determine the number of different triangles that can be drawn using the given angles, we need to consider the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Since we only have information about the angles, we cannot determine the exact lengths of the sides. However, we can still compare the angles to see if it is possible to construct a triangle.
Given that we have a 20 degree angle, a 45 degree angle, and a 155 degree angle, let's analyze the different cases:
1. If the 20 degree angle is the smallest angle:
In this case, the 45 degree angle will be the second largest angle, and the 155 degree angle will be the largest angle. To construct a triangle, the sum of the two smaller angles must be greater than the largest angle:
20 + 45 > 155
This equation is false, which means it is not possible to construct a triangle in this case.
2. If the 45 degree angle is the smallest angle:
In this case, the 20 degree angle will be the second largest angle, and the 155 degree angle will be the largest angle. Again, we need to check the triangle inequality:
45 + 20 > 155
This equation is false, so it is not possible to construct a triangle in this case either.
3. If the 155 degree angle is the smallest angle:
In this case, the 20 degree angle will be the second largest angle, and the 45 degree angle will be the largest angle. Checking the triangle inequality:
155 + 20 > 45
This equation is true, so it is possible to construct a triangle in this scenario.
Therefore, there is only one possible triangle that can be formed using the given angles: a triangle with angles measuring 20 degrees, 45 degrees, and 155 degrees.