Math Question
![Given: \( \angle B \) and \( \angle C \) form a linear pair, \( \angle A \cong \angle B \), and \( m \angle A=120^{\circ} \)
Prove: \( \mathrm{m} \angle \mathrm{C}=60^{\circ} \)
Statement: Reason:
1. \( \angle A \cong \angle B \quad \) 1. Given
2. \( m \angle A=m \angle B \quad \) 2. [ ? ]
3. \( \mathrm{m} \angle \mathrm{A}=120^{\circ} \quad \) 3. Given
4. \( 120^{\circ}=m \angle B \quad \) 4. Substitution
5. \( \angle \mathrm{B} \) and \( \angle \mathrm{C} \) form a \( \quad \) 5. Given
linear pair
6. \( \mathrm{m} \angle \mathrm{B}+\mathrm{m} \angle \mathrm{C}=180^{\circ} \quad \) 6. Linear Pair
Postulate
7. \( 120^{\circ}+\mathrm{m} \angle \mathrm{C}=180^{\circ} \quad \) 7. Substitution
8. \( \mathrm{m} \angle \mathrm{C}=60^{\circ} \)
\( 8 . \)](https://d3hlidq5bf9vg0.cloudfront.net/app-server-student/2022/4/14/4fe38920-bd43-4997-ace0-11caad932ceb.png "Given: \( \angle B \) and \( \angle C \) form a linear pair, \( \angle A \cong \angle B \), and \( m \angle A=120^{\circ} \)
Prove: \( \mathrm{m} \angle \mathrm{C}=60^{\circ} \)
Statement: Reason:
1. \( \angle A \cong \angle B \quad \) 1. Given
2. \( m \angle A=m \angle B \quad \) 2. [ ? ]
3. \( \mathrm{m} \angle \mathrm{A}=120^{\circ} \quad \) 3. Given
4. \( 120^{\circ}=m \angle B \quad \) 4. Substitution
5. \( \angle \mathrm{B} \) and \( \angle \mathrm{C} \) form a \( \quad \) 5. Given
linear pair
6. \( \mathrm{m} \angle \mathrm{B}+\mathrm{m} \angle \mathrm{C}=180^{\circ} \quad \) 6. Linear Pair
Postulate
7. \( 120^{\circ}+\mathrm{m} \angle \mathrm{C}=180^{\circ} \quad \) 7. Substitution
8. \( \mathrm{m} \angle \mathrm{C}=60^{\circ} \)
\( 8 . \)")
Solution
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