Answer: The missing step is Statement: [tex]m\angle 4 = m\angle 16[/tex], Reason: Transitive Property of Equality.
Explanation:
According to the given diagram ⇒ [tex]\angle 4\cong \angle8[/tex] and [tex]\angle 8\cong \angle16[/tex] (for parallel lines cut by transversal, corresponding angles are congruent)
⇒ [tex]m\angle 4= m\angle8[/tex] -------(1) (definition of congruent angles)
and [tex]m\angle 8= m\angle16[/tex] ---------(2) (definition of congruent angles)
From equation (1) and (2) [tex]m\angle 4 = m\angle 16[/tex] (Transitive Property of Equality)---(3)
Now, By linear pair theorem, [tex]\angle 15[/tex] and [tex]\angle 16[/tex] are supplementary angles.
Therefore, [tex]\angle 15+\angle 16=180[/tex] degree ------(4)
From equation (4) and (3),
[tex]\angle 15+\angle 4=180[/tex] degree
⇒[tex]\angle 15[/tex] and [tex]\angle 4[/tex] are supplementary angles.
