Question

9. Use the following triangles to answer the following. Assume AABC = ADEF. (2 points)

B
a.
(3x + 6) ft
14
(6y +12)°
A
25 ft
What is the length of AB?
(8y + 2)"
D
(4x) ft
E
b. What is mLEDF?

Answer 1

AB = 24 ft , ∠ EDF = 42°

Explanation:

since the triangles are congruent then corresponding sides and angles are congruent.

(a)

DE = AB , that is

4x = 3x + 6 ( subtract 3x from both sides )

x = 6

then

AB = 3x + 6 = 3(6) + 6 = 18 + 6 = 24 ft

(b)

∠ EDF = ∠ BAC , that is

8y + 2 = 6y + 12 ( subtract 6y from both sides )

2y + 2 = 12 ( subtract 2 from both sides )

2y = 10 ( divide both sides by 2 )

y = 5

then

∠ EDF = 8y + 2 = 8(5) + 2 = 40 + 2 = 42°