Question

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

1. statement 5: $x = 40$

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

Explanation:

Step1: Analyze the relationship between angles

Since \( \angle CDE=x^{\circ}\) and \( \angle EDF=(3x + 20)^{\circ}\) and \( \angle CDE+\angle EDF = 180^{\circ}\) (linear - pair of angles), we have the equation \(x+(3x + 20)=180\).
Simplifying the left - hand side gives \(4x+20 = 180\).
Using the Subtraction Property of Equality (\(a=b\Rightarrow a - c=b - c\)), we subtract 20 from both sides: \(4x+20-20=180 - 20\), so \(4x=160\).

Step2: Solve for \(x\)

Using the Division Property of Equality (\(a = b,c
eq0\Rightarrow\frac{a}{c}=\frac{b}{c}\)), we divide both sides of \(4x = 160\) by 4.
We have \(x=\frac{160}{4}=40\).

Answer:

C. Division Property of Equality