Question

Length of DE is ___

units.
Length of DB is ___
units.
Measure of angle FED is ___
degrees.

Answer 1

Length of DE = 7.5 units

Length of DB = 9.2 units

Measure of ∠FED = 82°

Explanation:

In ΔABC,

AD ≅ BD and CE ≅ BE [Given]

By the theorem of mid-segments,

DE =
`(1)/(2)(AC)`

=
`(1)/(2)(15)`

DE = 7.5 units

Since AD ≅ FE ≅ 9.2 [By midpoint theorem in ΔACB]

Therefore, length of DB = 9.2 units

[Although it's not given in the question, but we assume FE║AB]

Since FE║AB and DE is a transverse,

Therefore, m(∠FED) ≅ m(∠BDE) ≅ 82° [Interior alternate angles]