Question

1.
2.

1. using substitution, a + b = c + d
2. subtracting c from both sides, a + b - c = d.

b = g because they are corresponding angles. c + d = 180 because they are a linear pair. d = f + g because they are alternate interior angles. a + b = 180 because they are a linear pair.

Explanation:

Step1: Identify linear - pair property

Since \(a\) and \(b\) are a linear pair, \(a + b=180\). Also, since \(c\) and \(d\) are a linear pair, \(c + d = 180\).

Step2: Use substitution

Because \(a + b=180\) and \(c + d = 180\), we can substitute to get \(a + b=c + d\).

Step3: Perform subtraction

Subtract \(c\) from both sides of the equation \(a + b=c + d\) to isolate \(d\). We get \(a + b - c=d\).

Answer:

The key steps rely on the linear - pair property (sum of angles in a linear pair is 180) and substitution and subtraction operations on equations. The final result is \(a + b - c=d\).