Question

What is the missing step in the given proof?

Answer 1

Statement: ∠7 and ∠8 are supplementary.
Reason: Linear Pair Theorem

Answer 2

Answer: The missing step is Statement: $m\angle 4 = m\angle 16$,  Reason: Transitive Property of Equality.

Explanation:

According to the given diagram ⇒ $\angle 4\cong \angle8$ and $\angle 8\cong \angle16$ (for parallel lines cut by transversal, corresponding angles are congruent)

⇒ $m\angle 4= m\angle8$ -------(1) (definition of congruent angles)

and $m\angle 8= m\angle16$ ---------(2) (definition of congruent angles)

From equation (1) and (2) $m\angle 4 = m\angle 16$ (Transitive Property of Equality)---(3)

Now, By linear pair theorem, $\angle 15$ and $\angle 16$ are supplementary angles.

Therefore,   $\angle 15+\angle 16=180$ degree ------(4)

From equation (4) and (3),

$\angle 15+\angle 4=180$ degree

⇒$\angle 15$ and $\angle 4$ are supplementary angles.