# What is the missing step in the given proof?

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## Question:

What is the missing step in the given proof?

Statement: m∠4 = m∠15
Reason: Substitution Property of Equality
Statement: m∠4 + m∠8 = 180°
Reason: definition of supplementary angles
Statement: ∠7 and ∠8 are supplementary.
Reason: Linear Pair Theorem
Statement: m∠4 = m∠16
Reason: Transitive Property of Equality
Statement: ∠15 and ∠8 are supplementary.
Reason: Transitive Property of Equality

Answer: The missing step is Statement: ,  Reason: Transitive Property of Equality.

Explanation:

According to the given diagram ⇒ and (for parallel lines cut by transversal, corresponding angles are congruent)

——-(1) (definition of congruent angles)

and ———(2) (definition of congruent angles)

From equation (1) and (2) (Transitive Property of Equality)—(3)

Now, By linear pair theorem, and are supplementary angles.

Therefore,   degree ——(4)

From equation (4) and (3),

degree

and are supplementary angles.

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