Question

complete the proof that $m\angle g + m\angle f = 90^\circ$.

statement	reason
2. $m\angle h = 90^\circ$	definition of perpendicular lines
3. $m\angle f + m\angle g + m\angle h = 180^\circ$	triangle angle sum theorem
4. $m\angle f + m\angle g + 90^\circ = 180^\circ$	substitution
5. $m\angle g + m\angle f = 90^\circ$

Explanation:

Step1: Analyze the equation from Step 4

We have the equation \( m\angle F + m\angle G + 90^\circ = 180^\circ \) from Step 4.

Step2: Solve for \( m\angle F + m\angle G \)

To isolate \( m\angle F + m\angle G \), we subtract \( 90^\circ \) from both sides of the equation. Using the Subtraction Property of Equality, which states that if \( a + b = c \), then \( a + b - d = c - d \) (here \( a = m\angle F \), \( b = m\angle G \), \( c = 180^\circ \), \( d = 90^\circ \)), we get \( m\angle F + m\angle G = 180^\circ - 90^\circ = 90^\circ \). So the reason for Step 5 is the Subtraction Property of Equality (or Subtracting 90° from both sides of the equation).

Answer:

Subtraction Property of Equality (or Subtract \( 90^\circ \) from both sides of the equation)