Question

given: $m\angle edf = 120^{\circ},m\angle adb=(3x)^{\circ},m\angle bdc=(2x)^{\circ}$ prove: $x = 24$ what is the missing reason in step 3? statements reasons 1. $m\angle edf = 120^{\circ},m\angle adb=(3x)^{\circ},m\angle bdc=(2x)^{\circ}$ 1. given 2. $\angle edf$ and $\angle adc$ are vert. $\angle s$ 2. def. of vert. $\angle s$ 3. $\angle edf\cong\angle adc$ 3. ? 4. $m\angle adc=m\angle adb + m\angle bdc$ 4. $\angle$ add post 5. $m\angle edf=m\angle adc$ 5. def. of $\cong$ 6. $m\angle edf=m\angle adb + m\angle bdc$ 6. substitution 7. $120 = 3x+2x$ 7. substitution 8. $120 = 5x$ 8. addition 9. $x = 24$ 9. div prop of eq o vertical angles are congruent o substitution o definition of congruency o definition of equality

Explanation:

Step1: Recall vertical - angle property

Vertical angles are congruent. Since $\angle EDF$ and $\angle ADC$ are vertical angles, if $\angle EDF = 120^{\circ}$, then $\angle ADC=120^{\circ}$ because vertical angles are congruent.

Step2: Analyze step 3 in the proof

In step 3, we have $\angle EDF\cong\angle ADC$. The reason for this is that vertical angles are congruent.

Answer:

vertical angles are congruent