Which set of angle measures CANNOT be the angle measures of a triangle?
Responses
A 1.5 degrees, 1.5 degrees, 177 degrees1.5 degrees, 1.5 degrees, 177 degrees
B 13.9 degrees, 16.1 degrees, 150 degrees13.9 degrees, 16.1 degrees, 150 degrees
C 50 degrees,49.1 degrees, 80 degrees50 degrees,49.1 degrees, 80 degrees
D 58 degrees, 61 degrees, 61 degrees
A 1.5 degrees, 1.5 degrees, 177 degrees
To determine which set of angle measures cannot be the angle measures of a triangle, we need to apply the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees.
Let's go through each option and calculate the sum of the angles:
A. 1.5 degrees + 1.5 degrees + 177 degrees = 180 degrees
B. 13.9 degrees + 16.1 degrees + 150 degrees = 180 degrees
C. 50 degrees + 49.1 degrees + 80 degrees = 179.1 degrees (not equal to 180 degrees)
D. 58 degrees + 61 degrees + 61 degrees = 180 degrees
Since option C does not satisfy the Triangle Angle Sum Theorem, the set of angle measures 50 degrees, 49.1 degrees, 80 degrees cannot be the angle measures of a triangle.
Therefore, the correct answer is C. 50 degrees, 49.1 degrees, 80 degrees.