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° 1. given

m∠adb=(3x)°
m∠bdc=(2x)°

1. ∠edf and ∠adc are vert. ∠s 2. def of vert. ∠s
2. ∠edf≅∠adc 3.?
3. m∠adc = m∠adb + m∠bdc 4. ∠ add. post.
4. m∠edf = m∠adc 5. def of ≅
5. m∠edf = m∠adb + m∠bdc 6. substitution
6. 120 = 3x+2x 7. substitution
7. 120 = 5x 8. addition
8. x = 24 9. div prop of eq

vertical angles are congruent
substitution
definition of congruency
definition of equality

Explanation:

Step1: Identify vertical - angle property

Vertical angles are congruent. Since $\angle EDF$ and $\angle ADC$ are vertical angles, by the definition of vertical angles, they have equal measures.

Step2: Analyze step 3 in the proof

In step 3, we go from stating that $\angle EDF$ and $\angle ADC$ are vertical angles to $m\angle EDF=m\angle ADC$. This is because vertical angles are congruent, which means they have the same measure.

Answer:

vertical angles are congruent