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

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1. $m\angle edf=120^\circ$<br>$m\angle adb=(3x)^\circ$<br>$m\angle bdc=(2x)^\circ$

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.

- vertical angles are congruent- substitution- definition of congruency- definition of equality

Explanation:

Step 2 states that $\angle EDF$ and $\angle ADC$ are vertical angles. The reason that pairs of vertical angles are congruent is a fundamental geometric theorem, which directly justifies step 3's statement that $\angle EDF \cong \angle ADC$.

Answer:

vertical angles are congruent