Question

Fill in the missing reasons in the Two-column proof below.

Given: m∠2 + m∠3 + m∠4 = 180°
Prove: m∠1= m∠3 + m∠4

Statement Reasons
a. m∠2 + m∠3 + m∠4 = 180° a.
b. m∠1 + m∠2 = 180° b.
c. m∠1 + m∠2 = m∠2 + m∠3 + m∠4 c.
d. m∠1 + m∠2 - m∠2 = m∠2 + m∠3 + m∠4 -m∠2 d.
e. m∠1 = m∠3 + m∠4 e.

Answer 1

a. Given (This is part of the original problem)
b. Supplementary angles form 180 degrees (The definition of supplementary angles is that two or more angles have a sum of 180 degrees. DC is a straight line and has a measure of 180 degrees)
c. Substitution (Given the two previous statements, they are each equal to 180 degrees. Since 180=180 then you can substitute the angles in the equation.)
d. Subtraction (m<2 is being subtracted)
e. Subtraction postulate (Since the same quantity was being subtracted from each side of the equation, they are still equal)