Explain why the angle relationship shown are not possible
triangle angles
2x-15
3x-17
4x+12
If you did the math in this problem,the
sum of the angles would add up to 179.9998 deg. This is known as Hyberbolic Geometry. Read an article on
this type of geometry for more INFO.
not possible
To determine if the angle relationship shown is possible or not, we need to consider the properties of triangles. In a triangle, the sum of all three angles is always equal to 180 degrees.
Let's set up an equation using the given angle expressions:
2x - 15 + 3x - 17 + 4x + 12 = 180
Combine like terms:
9x - 20 = 180
Now, we'll solve for x:
9x = 180 + 20
9x = 200
x = 200/9
After calculating x, we can substitute the value back into the angle expressions to find the measures of the angles:
Angle 1 = 2(200/9) - 15
Angle 2 = 3(200/9) - 17
Angle 3 = 4(200/9) + 12
However, the problem lies in the possibility of obtaining a non-integer or decimal value for x. Since angles in a triangle must have measure in whole numbers, fractions, or decimals, it is not possible for the angle expressions to result in an angle measure that isn't an integer or a decimal that can be easily converted to a whole number.
Therefore, the angle relationship shown by the expressions 2x-15, 3x-17, 4x+12 is not possible because it would result in angle measures that do not conform to the properties of a triangle.