MATH SOLVE

2 months ago

Q:
# What is the missing step in the given proof?Statement: m∠4 = m∠15Reason: Substitution Property of EqualityStatement: m∠4 + m∠8 = 180°Reason: definition of supplementary anglesStatement: ∠7 and ∠8 are supplementary.Reason: Linear Pair TheoremStatement: m∠4 = m∠16Reason: Transitive Property of EqualityStatement: ∠15 and ∠8 are supplementary.Reason: Transitive Property of Equality

Accepted Solution

A:

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.