Question

given ( mangle edf = 120^{circ};mangle adb=(3x)^{circ},mangle bdc=(2x)^{circ} ) prove ( x = 24 ) what is the missing reason in step 3? statements reasons 1 ( mangle edf = 120^{circ} ) ( mangle adb=(3x)^{circ} ) ( mangle bdc=(2x)^{circ} ) 1 given 2 ( angle edf ) and ( angle adc ) are vert ( angle s ) 2 def of vert ( angle s ) 3 ( angle edfcongangle adc ) 3 ? 4 ( mangle adc=mangle adb + mangle bdc ) 4 ( angle ) add post 5 ( mangle edf=mangle adc ) 5 def of ( cong ) 6 ( mangle edf=mangle adb + mangle 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:

Vertical angles are formed when two lines intersect. By the vertical angles theorem, vertical angles are congruent. In step 2, it is stated that \(\angle EDF\) and \(\angle ADC\) are vertical angles. So, in step 3, the reason for \(\angle EDF\cong\angle ADC\) is that vertical angles are congruent.

Answer:

vertical angles are congruent