Question

given the image, choose the correct reason for each statement of the proof.

1. statement 4: ( 4x = 100 )

a. substitution property
b. angle addition postulate
c. division property of equality
d. simplify
e. subtraction property of equality

Explanation:

1. First, we know that \(\angle CDE\) and \(\angle EDF\) are adjacent angles that form a linear - pair (they are on a straight line \(CF\)). By the Angle Addition Postulate, \(\angle CDE+\angle EDF = 180^{\circ}\). So \(x+(3x + 20)=180\).
2. Then, simplify the left - hand side of the equation: \(x+3x + 20=(1 + 3)x+20=4x + 20\). So the equation becomes \(4x+20 = 180\).
3. Next, use the Subtraction Property of Equality. If \(a=b\), then \(a - c=b - c\). Subtract \(20\) from both sides of \(4x+20 = 180\): \(4x+20-20=180 - 20\), which gives \(4x=160 - 60=100\).

Answer:

E. Subtraction Property of Equality