Question

In ΔDEF, m∠D = 83° and m∠E = 11°. Which statement about the sides of ΔDEF must be true?

Answer 1

they are all acute angles

Answer 2

We're given D = 83 and E = 11. Let's find the missing angle F

D+E+F = 180

83+11+F = 180

94+F = 180

F = 180-94

F = 86

Since the triangle has angles

D = 83

E = 11

F = 86

We can say the following:

• FD is the shortest side (since it is opposite the smallest angle E = 11)
• ED is the longest side (since it is opposite the largest angle F = 86)

• That puts side EF as the medium length side of the triangle.
• All three angles of this triangle are less than 90, so this triangle is acute.
• Also, all three angles are different which makes this triangle scalene as well.