According to the Triangle Sum Theorem, the sum of the measures of the interior angles of a triangle is 180^(∘). Therefore, if the sum of a set of angles add up to 180^(∘), we know that set could form a triangle.
Set
Sum of Angles
Value of the Sum
A
100^(∘)+50^(∘)+40^(∘)
190^(∘) *
B
96^(∘)+74^(∘)+10^(∘)
180^(∘) ✓
C
165^(∘)+113^(∘)+82^(∘)
360^(∘) *
D
101^(∘)+41^(∘)+38^(∘)
180^(∘) ✓
E
90^(∘)+45^(∘)+45^(∘)
180^(∘) ✓
F
84^(∘)+62^(∘)+34^(∘)
180^(∘) ✓
The angles which add to 180^(∘) are the ones of choices B, D, E, and F.
