Question

if ( mangle a + mangle b = 88^{circ} ) and ( mangle a + mangle b + mangle c = 150^{circ} ), which property of equality will you use in the first step to find ( mangle c )?
substitution property of equality
symmetric property of equality
reflexive property of equality
transitive property of equality

Explanation:

To find \( m\angle C \), we know \( m\angle A + m\angle B = 88^\circ \) and \( m\angle A + m\angle B + m\angle C = 150^\circ \). The first step is to replace \( m\angle A + m\angle B \) in the second equation with its known value (\( 88^\circ \)) using the Substitution Property of Equality, which allows substituting a known equal quantity for its equivalent. The Symmetric Property (\( a = b \implies b = a \)), Reflexive Property (\( a = a \)), and Transitive Property (\( a = b, b = c \implies a = c \)) do not apply here.

Answer:

A. Substitution Property of Equality