Exercise 38 Page 593

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.