Given: mangleedf = 120°; mangleadb = (3x)°; manglebdc = (2x)° prove: x = 24 3 lines are shown. a line with points e, d, c intersects a line with points a, d, f at point d. a line extends from point d to point b in between angle a d c. angle e d f is 120 degrees, angle c d b is (2 x) degrees, and angle b d a is (3 x) degrees. what is the missing reason in step 3? a 2-column table has 9 rows. column 1 is labeled statements with entries measure of angle e d f = 120 degrees measure of angle a d b = (3 x) degrees measure of angle b d c = (2 x) degrees, angle e d f and angle a d c are vertical angles, angle e d f is-congruent-to angle a d c, measure of angle a d c = measure of angle a d b + measure of angle b d c, measure of angle e d f = measure of angle a d c, measure of angle e d f = measure of angle a d b + measure of angle b d c, 120 = 3 x + 2 x, 120 = 5 x, x = 24. column 2 is labeled reasons with entries given, def. of vert. angles, question mark, angle add. post., definition of congruency, substitution, substitution, addition, div, prop. of equality. vertical angles are congruent substitution definition of congruency definition of equality

" Vertical angles are congruent " ⇒ 2nd answer

Step-by-step explanation:

* Look to the attached figure

- 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