Question

iven: 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

Answer 1

"Vertical angles are congruent."

Reason: If two angles are vertical (formed by intersecting lines), they are congruent (have equal measures), so ∠EDF ≅ ∠ADC.