Answer:
" Vertical angles are congruent " ⇒ 2nd answer
Step-by-step explanation:
* <em>Look to the attached figure </em>
- There are three lines intersected at point D
- We need to find the missing in step 3
∵ Line FA intersects line EC at point D
- The angles formed when two lines cross each other are called
  vertical angles
- Vertical angles are congruent (vertical angles theorem)
∴ ∠ADC and ∠FDE are vertical angles
∵ Vertical angles are congruent
∴ ∠EDF ≅ ∠ADC
∴ m∠EDF ≅ m∠ADC
∵ m∠EDF = 120° ⇒ given
∵ m∠ADC = m∠ADB + m∠BDC
∴ m∠ADB + m∠BDC = 120°
∵ m∠ADB = (3x)° ⇒ given
∵ m∠BDC = (2x)° ⇒ given
∴ 3x + 2x = 120 ⇒ add like terms
∴ 5x = 120 ⇒ divide both sides by 5
∴ x = 24
 Column (1)                                                     Column (2)
 m∠EDF = 120°                                               given
 m∠ADB = 3 x                                                 given
 m∠BDC = 2 x                                                 given
 ∠EDF and ∠ADC are vertical angles           defin. of vert. ∠s
 ∠EDF is congruent to ∠ADC                        vertical angles are      
                                                                         congruent  
 m∠ADC = m∠ADB + m∠BDC                        angle add. post.
 m∠EDF = m∠ADC                                          defin. of cong.
 m∠EDF = m∠ADB + m∠BDC                         substitution 
 120° = 3 x + 2 x                                               substitution
 120 = 5 x                                                         addition
 x = 24                                                              division   
∴ The missing reason is " vertical angles are congruent "
- From the explanation above ∠ADC and ∠FDE are vertical 
  angles then they are congruent according to vertical angle 
  theorem