Question

duction to proof if ( mangle a = mangle b ) and ( mangle a + mangle c = mangle d ), then ( mangle b + mangle c = mangle d ). which property is shown? transitive property symmetric property reflexive property substitution property

Explanation:

We know \( m\angle A = m\angle B \) and \( m\angle A + m\angle C = m\angle D \). The substitution property allows replacing \( m\angle A \) with \( m\angle B \) in the second equation, giving \( m\angle B + m\angle C = m\angle D \). Other properties don't apply: transitive relates three equalities, symmetric swaps sides, reflexive is \( a = a \).

Answer:

substitution property