Final answer:
The question relates to solving for the missing angles in triangles using the property that the sum of angles in a triangle equals 180 degrees. For two of the provided sets, the angles do not sum up to 180, indicating they are not valid triangle angle measures.
Step-by-step explanation:
The student is asking to solve for x in various sets of triangle angle measures. To do so, we use the fundamental property that the sum of interior angles in a triangle always equals 180 degrees.
- (a) 20 degrees, 37 degrees, 58 degrees: To find the missing angle, we summarize the given angles and subtract from 180 degrees. x = 180 - (20 + 37 + 58) = 180 - 115 = 65 degrees.
- (b) 25 degrees, 45 degrees, 65 degrees: Similarly, x = 180 - (25 + 45 + 65) = 180 - 135 = 45 degrees.
- (c) 30 degrees, 55 degrees, 95 degrees: We follow the same process to find x = 180 - (30 + 55 + 95) = 0 degrees, which indicates an error because a triangle cannot have an angle of 0 degrees.
- (d) 35 degrees, 65 degrees, 85 degrees: Again, by the same method, x = 180 - (35 + 65 + 85) = 180 - 185 = -5 degrees, which is not possible, indicating an error.
In case (c) and (d), the provided angles do not form valid triangles because the sum of the angles does not equal 180 degrees, or one of the angles given is impossible (i.e., negative or zero).