Question

given: m∠edf = 120°; m∠adb=(3x)°; m∠bdc=(2x)° prove: x = 24 what is the missing reason in step 3? statements reasons 1. m∠edf = 120° m∠adb=(3x)° m∠bdc=(2x)° 1. given 2. ∠edf and ∠adc are vert. ∠s ∠edf ≅ ∠adc 2. def of vert. ∠s 3.? 4. m∠adc = m∠adb + m∠bdc 4. ∠ add. post 5. m∠edf = m∠adc 5. def of ≅ 6. m∠edf = m∠adb + m∠bdc 6. substitution 7. 120 = 3x+2x 7. substitution 8. 120 = 5x 8. addition 9. x = 24 9. div prop of = vertical angles are congruent substitution definition of congruency definition of equality

Explanation:

In step 3, since ∠EDF and ∠ADC are vertical - angles, by the property that vertical angles are congruent, we can say ∠EDF ≅ ∠ADC.

Answer:

vertical angles are congruent