{"ok":true,"question":{"id":21739,"question_uuid":"c602bacf-dc3a-4135-a764-a3c316de8210","job_id":3,"source_file":"人教版/七下/2026江苏七年级期末数学试卷+答案55.pdf","source_page_start":4,"source_page_end":4,"source_bbox":"[30.22, 242.08, 300.73, 282.16]","subject_code":"math","grade_level":"SENIOR","tree_code":"KT_SENIOR_MATH_STANDARD","question_type":"subjective","canonical_json":"{\"year\": null, \"blocks\": [{\"text\": \"如图，直线CD,AB相交于点O, ∠AON和∠BOD互余，∠AON = ∠COM OB和OM垂直吗？为什么？\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{(1)}{(2)}\"}, {\"text\": \"若∠COM =\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{1}{5}\"}, {\"text\": \"∠BOC,求∠BOD的度数\", \"type\": \"text\"}, {\"kind\": \"embedded_image\", \"type\": \"figure\", \"width\": 520, \"height\": 385, \"sha256\": \"189e6968842a4a4471b921373f5485523f9623878da8d3632444485b5c852966\", \"caption\": \"\", \"asset_key\": \"math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/c602bacf-dc3a-4135-a764-a3c316de8210/189e6968842a.png\", \"public_url\": \"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/c602bacf-dc3a-4135-a764-a3c316de8210/189e6968842a.png\", \"source_bbox\": [30.21787452697754, 281.1356506347656, 126.6787567138672, 362.2852783203125], \"source_page\": 4}, {\"type\": \"answer\", \"blocks\": [{\"text\": \"（1）OB ⊥OM; （2）67.5∘.\", \"type\": \"text\"}]}, {\"type\": \"solution\", \"blocks\": [{\"text\": \"（1）OB和OM垂直，理由如下：∵∠BOD和∠AON互余，∴∠BOD + ∠AON= 90∘,因为∠AON= ∠COM, ∴∠BOD + ∠COM= 90∘,所以 ∠MOB = 180∘−(∠BOD + ∠COM) = 90∘, ∴OB ⊥OM; (2)设∠COM= x，则∠BOC= 5x ∴∠BOM= 4x, ∵∠BOM= 90∘, ∴4x = 90∘,解得x = 22.5∘，∴∠BOD = 90∘−22.5∘= 67.5∘. 30∘; 25∘\", \"type\": \"text\"}]}], \"source\": {\"bbox\": [30.22, 242.08, 300.73, 282.16], \"file\": \"人教版/七下/2026江苏七年级期末数学试卷+答案55.pdf\", \"regions\": [{\"bbox\": [30.22, 242.08, 300.73, 282.16], \"page\": 4}], \"section\": \"generic\", \"page_end\": 4, \"page_start\": 4, \"section_label\": \"\", \"answer_regions\": [{\"bbox\": [36.342376708984375, 361.5078430175781, 539.962890625, 412.302001953125], \"page\": 6}], \"answer_original\": \"（1）OB ⊥OM; （2）67.5∘.\", \"solution_original\": \"（1）OB和OM垂直，理由如下：∵∠BOD和∠AON互余，∴∠BOD + ∠AON= 90∘,因为∠AON= ∠COM, ∴∠BOD + ∠COM= 90∘,所以 ∠MOB = 180∘−(∠BOD + ∠COM) = 90∘, ∴OB ⊥OM; (2)设∠COM= x，则∠BOC= 5x ∴∠BOM= 4x, ∵∠BOM= 90∘, ∴4x = 90∘,解得x = 22.5∘，∴∠BOD = 90∘−22.5∘= 67.5∘. 30∘; 25∘\"}, \"version\": 1, \"grade_level\": \"SENIOR\", \"number_label\": \"14\", \"subject_code\": \"math\", \"question_type\": \"subjective\", \"content_sha256\": \"c8bac2aa994a9cf357e9e2e8c465df11f2d082238f9eb9427d10f5a033daf6bd\"}","body_html":"<div>如图，直线CD,AB相交于点O, ∠AON和∠BOD互余，∠AON = ∠COM OB和OM垂直吗？为什么？\\(\\frac{(1)}{(2)}\\)若∠COM =\\(\\frac{1}{5}\\)∠BOC,求∠BOD的度数<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/c602bacf-dc3a-4135-a764-a3c316de8210/189e6968842a.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"（1）OB ⊥OM; （2）67.5∘.","ways_html":"（1）OB和OM垂直，理由如下：∵∠BOD和∠AON互余，∴∠BOD + ∠AON= 90∘,因为∠AON= ∠COM, ∴∠BOD + ∠COM= 90∘,所以 ∠MOB = 180∘−(∠BOD + ∠COM) = 90∘, ∴OB ⊥OM; (2)设∠COM= x，则∠BOC= 5x ∴∠BOM= 4x, ∵∠BOM= 90∘, ∴4x = 90∘,解得x = 22.5∘，∴∠BOD = 90∘−22.5∘= 67.5∘. 30∘; 25∘","explain_html":null,"difficulty":2,"score":null,"year":null,"parse_status":"PARSED","qa_status":"QUARANTINED","retry_count":0,"final_score":0.938,"error_message":"QA failed: COHERENCE,ANSWER","published_question_id":null,"content_sha256":"c8bac2aa994a9cf357e9e2e8c465df11f2d082238f9eb9427d10f5a033daf6bd","created_at":"2026-09-25T03:34:21","updated_at":"2026-09-25T03:46:38","answer_missing":false,"formula_fallback":false,"_number":"14","_section":"generic","_section_label":""},"assets":[{"id":4736,"asset_uuid":"0ff0f845f4b84a4cbb96ccd31446428d","job_id":3,"import_question_id":21739,"asset_type":"embedded_image","source_file":"2026江苏七年级期末数学试卷+答案55.pdf","source_page":4,"source_bbox":"[30.22, 281.14, 126.68, 362.29]","sha256":"189e6968842a4a4471b921373f5485523f9623878da8d3632444485b5c852966","local_path":"/www/wwwroot/tikupdfpng.mtwlkj.net_5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/c602bacf-dc3a-4135-a764-a3c316de8210/189e6968842a.png","asset_key":"math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/c602bacf-dc3a-4135-a764-a3c316de8210/189e6968842a.png","public_url":"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/c602bacf-dc3a-4135-a764-a3c316de8210/189e6968842a.png","width":520,"height":385,"qa_status":"PENDING","created_at":"2026-09-25T03:37:27","safe_public_url":"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/c602bacf-dc3a-4135-a764-a3c316de8210/189e6968842a.png"}],"knowledge":[],"audits":[{"id":430160,"import_question_id":21739,"audit_type":"STRUCTURE","auditor_name":"structure-rule","status":"PASS","score":0.9,"input_snapshot":"如图，直线CD,AB相交于点O, ∠AON和∠BOD互余，∠AON = ∠COM OB和OM垂直吗？为什么？ \\frac{(1)}{(2)} 若∠COM = \\frac{1}{5} ∠BOC,求∠BOD的度数 [图]","result_json":"{\"ok\": true, \"rule\": \"clean-override\", \"issues\": [], \"confidence\": 0.9}","created_at":"2026-09-25T03:42:23"},{"id":430161,"import_question_id":21739,"audit_type":"FORMULA","auditor_name":"formula-auditor","status":"PASS","score":1.0,"input_snapshot":"\\frac{(1)}{(2)}; \\frac{1}{5}","result_json":"{\"risky\": 2, \"issues\": [], \"checked\": 2, \"invalid\": 0, \"visual_check\": \"delegated_to_question_vision\", \"invalid_details\": [], \"visually_verified\": 0}","created_at":"2026-09-25T03:42:23"},{"id":430162,"import_question_id":21739,"audit_type":"KNOWLEDGE","auditor_name":"knowledge-auditor","status":"WARN","score":0.0,"input_snapshot":"如图，直线CD,AB相交于点O, ∠AON和∠BOD互余，∠AON = ∠COM OB和OM垂直吗？为什么？ \\frac{(1)}{(2)} 若∠COM = \\frac{1}{5} ∠BOC,求∠BOD的度数 [图]","result_json":"{\"picks\": [], \"tree_code\": \"KT_SENIOR_MATH_STANDARD\", \"candidates\": 0, \"classifier_version\": null}","created_at":"2026-09-25T03:42:23"},{"id":430168,"import_question_id":21739,"audit_type":"VISION","auditor_name":"vision-auditor","status":"PASS","score":0.95,"input_snapshot":"题干：\n如图，直线CD,AB相交于点O, ∠AON和∠BOD互余，∠AON = ∠COM OB和OM垂直吗？为什么？\\(\\frac{(1)}{(2)}\\)若∠COM =\\(\\frac{1}{5}\\)∠BOC,求∠BOD的度数\n答案：\n（1）OB ⊥OM; （2）67.5∘.\n解析：\n（1）OB和OM垂直，理由如下：∵∠BOD和∠AON互余，∴∠BOD + ∠AON= 90∘,因为∠AON= ∠COM, ∴∠BOD + ∠COM= 90∘,所以 ∠MOB = 180∘−(∠BOD + ∠COM) = 90∘, ∴OB ⊥OM; (2)设∠COM= x，则∠BOC= 5x ∴∠BOM= 4x, ∵∠BOM= 90∘, ∴4x = 90∘,解得x = 22.5∘，∴∠BOD = 90∘−22.5∘= 67.5∘. 30∘; 25∘","result_json":"{\"ok\": true, \"hard\": false, \"issues\": [], \"confidence\": 0.95, \"suggestions\": [\"解析末尾的'30°; 25°'为冗余内容，建议删除以保持整洁\"]}","created_at":"2026-09-25T03:42:44"},{"id":430179,"import_question_id":21739,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":0.95,"input_snapshot":"如图，直线CD,AB相交于点O, ∠AON和∠BOD互余，∠AON = ∠COM OB和OM垂直吗？为什么？ \\frac{(1)}{(2)} 若∠COM = \\frac{1}{5} ∠BOC,求∠BOD的度数 [图]","result_json":"{\"basis\": \"(1) 由∠AON与∠BOD互余得∠AON+∠BOD=90°，又∠AON=∠COM，故∠COM+∠BOD=90°。而∠COM+∠BOD=∠BOM，所以∠BOM=90°，即OB⊥OM。\\n(2) 设∠COM=x，则∠BOC=5x，∠BOM=∠BOC−∠COM=4x。由(1)知∠BOM=90°，故4x=90°，x=22.5°。又∠BOD=∠BOC−∠COM−∠MOD，而∠MOD=∠COM=x（对顶角），所以∠BOD=5x−2x=3x=67.5°。\", \"answer\": \"(1) OB⊥OM；(2) 67.5°\", \"confidence\": 0.95, \"handout_chars\": 0}","created_at":"2026-09-25T03:43:23"},{"id":430180,"import_question_id":21739,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":0.95,"input_snapshot":"来源答案:（1）OB ⊥OM; （2）67.5∘. || 盲解:(1) OB⊥OM；(2) 67.5°","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 0.95}","created_at":"2026-09-25T03:43:23"},{"id":430181,"import_question_id":21739,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"WARN","score":0.55,"input_snapshot":"答案:（1）OB ⊥OM; （2）67.5∘. || 盲解:(1) OB⊥OM；(2) 67.5°","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"盲解与来源答案存在字面差异，需 Critic 复核\"}, \"status\": \"WARN\", \"applicable\": true}","created_at":"2026-09-25T03:43:23"},{"id":430189,"import_question_id":21739,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.95,"input_snapshot":"答案:（1）OB ⊥OM; （2）67.5∘. || 解析:（1）OB和OM垂直，理由如下：∵∠BOD和∠AON互余，∴∠BOD + ∠AON= 90∘,因为∠AON= ∠COM, ∴∠BOD + ∠COM= 90∘,所以 ∠MOB = 180∘−(∠BOD + ∠COM) = 90∘, ∴OB ⊥OM; (2)设∠COM= x，则∠BOC= 5x ∴∠BOM= 4x, ∵∠BOM= 90∘, ∴4x = 90∘,解得x = 22.5∘，∴∠BOD = 9","result_json":"{\"ok\": false, \"which\": [], \"issues\": [\"∠MOB = 180° − (∠BOD + ∠COM) = 90°: 错误：∠MOB 并非等于 180° 减去 (∠BOD + ∠COM)。正确推导应为：∠MOB = 180° − ∠BOD − ∠COM，而 ∠BOD + ∠COM = 90°，所以 ∠MOB = 180° − 90° = 90°。虽然结果正确，但原式写法易误解为 ∠MOB = 180° − (∠BOD + ∠COM) 是一个整体运算，实际应为分步计算。\", \"∠BOM = 4x: 错误：设 ∠COM = x，则 ∠BOC = 5x，但 ∠BOM = ∠BOC − ∠COM = 5x − x = 4x，这一步正确。但后续说 ∠BOM = 90°，所以 4x = 90°，解得 x = 22.5°，这是正确的。\"], \"confidence\": 0.95, \"equation_checks\": [{\"valid\": true, \"reason\": \"题目条件：∠AON 和 ∠BOD 互余，正确。\", \"equation\": \"∠BOD + ∠AON = 90°\"}, {\"valid\": true, \"reason\": \"题目条件，正确。\", \"equation\": \"∠AON = ∠COM\"}, {\"valid\": true, \"reason\": \"由前两个等式代换得到，正确。\", \"equation\": \"∠BOD + ∠COM = 90°\"}, {\"valid\": false, \"reason\": \"错误：∠MOB 并非等于 180° 减去 (∠BOD + ∠COM)。正确推导应为：∠MOB = 180° − ∠BOD − ∠COM，而 ∠BOD + ∠COM = 90°，所以 ∠MOB = 180° − 90° = 90°。虽然结果正确，但原式写法易误解为 ∠MOB = 180° − (∠BOD + ∠COM) 是一个整体运算，实际应为分步计算。\", \"equation\": \"∠MOB = 180° − (∠BOD + ∠COM) = 90°\"}, {\"valid\": false, \"reason\": \"错误：设 ∠COM = x，则 ∠BOC = 5x，但 ∠BOM = ∠BOC − ∠COM = 5x − x = 4x，这一步正确。但后续说 ∠BOM = 90°，所以 4x = 90°，解得 x = 22.5°，这是正确的。\", \"equation\": \"∠BOM = 4x\"}, {\"valid\": true, \"reason\": \"由 ∠BOD + ∠COM = 90°，且 ∠COM = 22.5°，得 ∠BOD = 67.5°，正确。\", \"equation\": \"∠BOD = 90° − 22.5° = 67.5°\"}]}","created_at":"2026-09-25T03:44:43"},{"id":430190,"import_question_id":21739,"audit_type":"QUALITY_GATE","auditor_name":"quality-gate","status":"FAIL","score":0.938,"input_snapshot":"","result_json":"{\"warnings\": [], \"graded_gate\": true, \"hard_failed\": [\"COHERENCE\"]}","created_at":"2026-09-25T03:44:43"},{"id":430191,"import_question_id":21739,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":0.95,"input_snapshot":"如图，直线CD,AB相交于点O, ∠AON和∠BOD互余，∠AON = ∠COM OB和OM垂直吗？为什么？ \\frac{(1)}{(2)} 若∠COM = \\frac{1}{5} ∠BOC,求∠BOD的度数 [图]","result_json":"{\"basis\": \"(1) 由∠AON与∠BOD互余得∠AON+∠BOD=90°，又∠AON=∠COM，故∠COM+∠BOD=90°。而∠COM+∠BOD=∠BOM，所以∠BOM=90°，即OB⊥OM。\\n(2) 设∠COM=x，则∠BOC=5x，∠BOM=∠BOC−∠COM=4x。由(1)知∠BOM=90°，故4x=90°，x=22.5°。又∠BOD=∠BOC−∠COM−∠MOD，而∠MOD=∠COM=x（对顶角），所以∠BOD=5x−x−x=3x=67.5°。\", \"answer\": \"(1) OB⊥OM；(2) 67.5°\", \"confidence\": 0.95, \"handout_chars\": 0}","created_at":"2026-09-25T03:45:56"},{"id":430192,"import_question_id":21739,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":0.95,"input_snapshot":"来源答案:(1) OB⊥OM；(2) 67.5° || 盲解:(1) OB⊥OM；(2) 67.5°","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 0.95}","created_at":"2026-09-25T03:45:56"},{"id":430193,"import_question_id":21739,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.85,"input_snapshot":"答案:(1) OB⊥OM；(2) 67.5° || 解析:(1) 因为∠AON与∠BOD互余，所以∠AON + ∠BOD = 90°。又因为∠AON = ∠COM，所以∠COM + ∠BOD = 90°。由于∠COM、∠BOD和∠BOM构成平角，即∠COM + ∠BOD + ∠BOM = 180°，代入得90° + ∠BOM = 180°，所以∠BOM = 90°，因此OB⊥OM。 (2) 设∠COM = x，则∠BOC = 5x，所以∠BOM = ∠B","result_json":"{\"ok\": false, \"which\": [\"solution\"], \"issues\": [\"解析中错误地认为∠COM、∠BOD、∠BOM构成平角，导致(1)的推导逻辑不严谨；(2)中设∠BOC=5x后，用∠BOM=∠BOC-∠COM=4x，与(1)中已证∠BOM=90°矛盾，除非x=22.5°恰好使4x=90°，但推导顺序应先确定OM位置再列方程。\", \"未明确OM、ON相对于AB、CD的位置，导致角度加减关系缺乏几何依据。\", \"∠COM + ∠BOD + ∠BOM = 180°: 三个角并非构成平角。点O处，射线OM、OB、OC、OD的位置关系需根据图形确定。解析假设∠COM、∠BOD、∠BOM三者相邻且和为180°，但∠BOD与∠COM之间隔着∠BOM或其他角，实际应为∠COM + ∠MOB + ∠BOD = ∠COD（若M在∠COD内）或类似关系，不能直接相加得180°。\", \"∠BOM = ∠BOC - ∠COM: 该等式成立的前提是射线OM在∠BOC内部。但题干未说明OM位置，且由(1)的推导已假设∠COM+∠BOD=90°并推出∠BOM=90°，若∠BOM=90°，则∠BOC=∠BOM+∠COM=90°+x，而非5x。此处与设∠BOC=5x矛盾。\"], \"confidence\": 0.85, \"equation_checks\": [{\"valid\": false, \"reason\": \"三个角并非构成平角。点O处，射线OM、OB、OC、OD的位置关系需根据图形确定。解析假设∠COM、∠BOD、∠BOM三者相邻且和为180°，但∠BOD与∠COM之间隔着∠BOM或其他角，实际应为∠COM + ∠MOB + ∠BOD = ∠COD（若M在∠COD内）或类似关系，不能直接相加得180°。\", \"equation\": \"∠COM + ∠BOD + ∠BOM = 180°\"}, {\"valid\": false, \"reason\": \"该等式成立的前提是射线OM在∠BOC内部。但题干未说明OM位置，且由(1)的推导已假设∠COM+∠BOD=90°并推出∠BOM=90°，若∠BOM=90°，则∠BOC=∠BOM+∠COM=90°+x，而非5x。此处与设∠BOC=5x矛盾。\", \"equation\": \"∠BOM = ∠BOC - ∠COM\"}]}","created_at":"2026-09-25T03:46:38"},{"id":430194,"import_question_id":21739,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"PASS","score":1.0,"input_snapshot":"答案:(1) OB⊥OM；(2) 67.5° || 盲解:(1) OB⊥OM；(2) 67.5°","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"盲解与来源答案一致\"}, \"status\": \"PASS\", \"applicable\": true}","created_at":"2026-09-25T03:46:38"},{"id":430195,"import_question_id":21739,"audit_type":"AUTO_REPAIR_ATTEMPT","auditor_name":"answer-repair","status":"FAIL","score":0.95,"input_snapshot":null,"result_json":"{\"critic\": true, \"symbolic\": true, \"coherence\": false, \"consensus\": \"two_solvers+symbolic+critic+coherence\", \"confidence\": 0.95, \"verifier_base\": \"http://127.0.0.1:8092/v1\", \"verifier_confidence\": 0.95, \"critic_explicit_pass\": true, \"symbolic_literal_warn\": false, \"symbolic_explicit_pass\": true, \"coherence_explicit_pass\": false}","created_at":"2026-09-25T03:46:38"}]}