Question

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

Explanation:

The problem involves replacing \( m\angle A \) with \( m\angle B \) in the equation \( m\angle A + m\angle C = m\angle D \) because \( m\angle A = m\angle B \). This matches the substitution property, where if two quantities are equal, one can be substituted for the other in an equation. The transitive property relates to equality of three quantities (\( a = b \), \( b = c \) implies \( a = c \)), symmetric is \( a = b \) implies \( b = a \), and reflexive is \( a = a \), none of which apply here.

Answer:

substitution property