Question

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

Explanation:

The substitution property states that if two quantities are equal, one can be substituted for the other in an equation. Here, since \( m\angle A = m\angle B \), we substitute \( m\angle A \) with \( m\angle B \) in the equation \( m\angle A + m\angle C = m\angle D \), resulting in \( m\angle B + m\angle C = m\angle D \). The reflexive property is \( a = a \), symmetric is if \( a = b \) then \( b = a \), and transitive is if \( a = b \) and \( b = c \) then \( a = c \), so those don't apply here.

Answer:

B. substitution property