Question

given
m∠1 + m∠2 = 120°
m∠3 + m∠4 = 120°
∠2 ≅ ∠3
prove
∠1 ≅ ∠4
statement

1. m∠1 + m∠2 = 120°
2. m∠3 + m∠4 = 120°
3. m∠1 + m∠2 = m∠3 + m∠4
4. ∠2 ≅ ∠3
5. m∠2 = m∠3
6. m∠1 + m∠2 = m∠2 + m∠4
7. m∠1 = m∠4
8. ∠1 ≅ ∠4

reason

1. given
2. given
3. substitution
4. given
5. definition of congruency
6. substitution
7. ?
8. definition of congruency

Explanation:

Step1: Analyze the equation \(m\angle1 + m\angle2=m\angle2 + m\angle4\)

We have \(m\angle1 + m\angle2=m\angle2 + m\angle4\).

Step2: Apply the subtraction property of equality

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

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Answer:

Subtraction Property of Equality