Final answer:
The sum of any two angles in a triangle is always greater than the third angle because the total sum of angles in a triangle is 180 degrees. For example, if angle A measures 60 degrees and angle B measures 80 degrees, their sum is 140 degrees, which is greater than angle C as long as angle C is less than 40 degrees.
Step-by-step explanation:
The sum of any two angles in a triangle is indeed greater than the third angle. This is because the sum of all three angles in a triangle is always 180 degrees. If you take any two angles and add them up, their sum must be less than 180 degrees since each angle in a triangle is positive. Therefore, the remaining third angle must be less than the sum of the other two angles.
For instance, if one angle in a triangle is 60 degrees and another is 70 degrees, their sum is 130 degrees. Since the total sum of angles must be 180 degrees, the third angle has to be 50 degrees, which is less than the sum of the 60 and 70-degree angles.