The completed statement and reason to prove the same side interior angles are supplementary m∠BFE + m∠DBF = 180°, is presented in the attached table with the values as follows;
Reasons Statements
m∠CBD=m∠BFE Given
m∠CBD+m∠DBF=180° Angles that form a linear pair are supplementary
m∠BFE+m∠DBF=180° Substitution property
What are same side interior angles; Same side interior angles are angles formed on the same side of a transversal and on the inside of the parallel lines.
The details of the reasons used to prove the angles are supplementary are as follows;
Angles that form a linear pair are supplementary
Linear pair angle are adjacent angles that combine together to form a line. The angle on a line is 180°, therefore, the angles formed by a linear pair angle are 180°, and are therefore supplementary angles
Substitution property
The substitution property states that if a = b then b can substitute a in an equation and the equation remains valid