Question

given
$m\angle1 + m\angle2 = 120^{\circ}$
$m\angle3 + m\angle4 = 120^{\circ}$
$\angle2\cong\angle3$
prove
$\angle1\cong\angle4$
statement

1. $m\angle1 + m\angle2 = 120^{\circ}$
2. $m\angle3 + m\angle4 = 120^{\circ}$
3. $m\angle1 + m\angle2 = m\angle3 + m\angle4$
4. $\angle2\cong\angle3$
5. $m\angle2 = m\angle3$
6. $m\angle1 + m\angle2 = m\angle2 + m\angle4$
7. $m\angle1 = m\angle4$
8. $\angle1\cong\angle4$

reason

1. given
2. given
3. substitution
4. given
5. definition of congruency
6. substitution

7)

1. definition of congruency

Explanation:

Step1: Analyze the equation in step 6

From step 6: \(m\angle1 + m\angle2=m\angle2 + m\angle4\).

Step2: Apply the subtraction property of equality

Subtract \(m\angle2\) from both sides of the equation \(m\angle1 + m\angle2=m\angle2 + m\angle4\).

$$
LATEXBLOCK0
$$

Answer:

Subtraction Property of Equality