given
$\angle 1$ and $\angle 2$ form a linear pair
$\angle 2$ and $\angle 3$ form a linear pair
$m\angle 1 = 120^\circ$

prove
$m\angle 3 = 120^\circ$

statement | reason
1) $\angle 1$ and $\angle 2$ form a linear pair | 1) given
2) $m\angle 1 + m\angle 2 = 180^\circ$ | 2) ?
3) $\angle 2$ and $\angle 3$ form a linear pair | 3) given
4) $m\angle 2 + m\angle 3 = 180^\circ$ | 4) linear pair postulate
5) $m\angle 1 + m\angle 2 = m\angle 2 + m\angle 3$ | 5) substitution property
6) $m\angle 1 = m\angle 3$ | 6)

Question

given
$\angle 1$ and $\angle 2$ form a linear pair
$\angle 2$ and $\angle 3$ form a linear pair
$m\angle 1 = 120^\circ$

prove
$m\angle 3 = 120^\circ$

statement | reason
1) $\angle 1$ and $\angle 2$ form a linear pair | 1) given
2) $m\angle 1 + m\angle 2 = 180^\circ$ | 2) ?
3) $\angle 2$ and $\angle 3$ form a linear pair | 3) given
4) $m\angle 2 + m\angle 3 = 180^\circ$ | 4) linear pair postulate
5) $m\angle 1 + m\angle 2 = m\angle 2 + m\angle 3$ | 5) substitution property
6) $m\angle 1 = m\angle 3$ | 6)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor" ], "needs_drawing": false, "concepts_used": [ "Algebraic Proof" ], "new_concepts": [ "Linear Pair Postulate" ], "current_concepts": [ "Algebraic Proof", "Linear Pair Postulate" ] } ## Identify the missing reason We need to find the missing reason for step 2 in the geometric proof. The statement is: $ \angle 1 $ and $ \angle 2 $ form a linear pair. The next statement is: $ m\angle 1 + m\angle 2 = 180^\circ $. ## Apply geometric definitions Using **Algebraic Proof** principles, we look at the relationship between a linear pair and their measures. By definition, angles in a linear pair are supplementary, meaning their measures add up to $ 180^\circ $. This is justified by the Linear Pair Postulate. ## Match with options Looking at the visible options on the right side of the screen: - Division Property - Linear Pair Postulate - Subtraction Property - Transitive Property The correct reason for step 2 is the Linear Pair Postulate. The missing reason for step 2 is Linear Pair Postulate. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Linear Pair Postulate" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the missing reason

Apply geometric definitions

Match with options

Answer: