calculate the value of r.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor" ], "needs_drawing": true, "concepts_used": [ "Linear Pair" ], "new_concepts": [ "Angles on a Straight Line", "Vertical Angles" ], "current_concepts": [ "Linear Pair", "Angles on a Straight Line", "Vertical Angles" ] } ## Identify the straight line The diagram shows intersecting lines. The line running from the bottom-left to the top-right is a straight line. ## Set up the angle equation Using the **Linear Pair** concept extended to multiple adjacent angles on a straight line, the angles on one side of this straight line must add up to $180^\circ$. $$ r^\circ + 62^\circ + 45^\circ = 180^\circ $$ ## Solve for r Combine the known values and subtract from $180$. $$ r + 107 = 180 $$ $$ r = 73 $$ Calculate the value of r. 73 { "elements": [ { "type": "line", "params": [[-5, -2.5], [5, 2.5]], "properties": { "strokeColor": "#583C87", "strokeWidth": 2 } }, { "type": "line", "params": [[-5, 2.5], [5, -2.5]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2 } }, { "type": "line", "params": [[0, 0], [0, 4]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "text", "params": [-0.8, 1.0, "$$r^\circ$$"], "properties": { "color": "#8C55F2" } }, { "type": "text", "params": [0.8, 0.8, "$$62^\circ$$"], "properties": { "color": "#F2557F" } }, { "type": "text", "params": [1.5, 0.1, "$$45^\circ$$"], "properties": { "color": "#F28A55" } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Angles on a Straight Line" ] }

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Question

Explanation:

Identify the straight line

Set up the angle equation

Solve for r

Answer: