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Includes multiple items with coordinate-like labels (X, M, Q, R, L) and an explicit condition that angle XQR equals 180° to guide the setup.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/finding-variable-value-by-balancing-equations-worksheet/466605/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/finding-variable-value-by-balancing-equations-worksheet/466605.png","ImageObject",300,407,{"name":42,"@type":43},"Liam","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-30","2026-09-30",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",5,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you determine the values of a and b in these problems?","Question",{"text":63,"@type":64},"Set up balanced equations using the given expressions and relationships, then solve the resulting linear system for a and b.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What role does the condition “Angle XQR is 180°” play?",{"text":68,"@type":64},"It provides the geometric constraint used to form or justify the equation relationships among the labeled parts.",{"name":70,"@type":61,"acceptedAnswer":71},"Where are the correct answers provided?",{"text":72,"@type":64},"An “Answer Key” section lists the solved values for each numbered item.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},466605,1792833742,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":55,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":30,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":110},8796095461564,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Finding Variable Value by Balancing Equations  \nName:  \n\n| Find the value of 'a' and 'b'. Angle XQR is 180°. |  |  | X\u003Cbr>M\u003Cbr>Q R\u003Cbr>\u003Cbr>-5b + 53\u003Cbr>-8a + 169\u003Cbr>\u003Cbr>61-9b\u003Cbr>L\u003Cbr>\u003Cbr>-5a + 157\u003Cbr>X\u003Cbr>\u003Cbr>R\u003Cbr> 129\u003Cbr>\u003Cbr>L\u003Cbr>\u003Cbr>\u003Cbr> 139\u003Cbr>2a + 42\u003Cbr>X\u003Cbr>-8a + 152\u003Cbr> M\u003Cbr>Q\u003Cbr>\u003Cbr>86-5b\u003Cbr>R\u003Cbr>\u003Cbr>X\u003Cbr>M\u003Cbr>Q R\u003Cbr>\u003Cbr>15 + 5b\u003Cbr>-6a + 142\u003Cbr>\u003Cbr>-2b + 64\u003Cbr> L\u003Cbr>\u003Cbr>\u003Cbr>126 + 2a |  |  | Answers\u003Cbr>1.    \u003Cbr>2.    \u003Cbr>3.    \u003Cbr>4.    \u003Cbr>5.    \u003Cbr>6.    \u003Cbr>7.    \u003Cbr>8.     |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1)\u003Cbr>3)\u003Cbr>5)\u003Cbr>7) | Q\u003Cbr>X\u003Cbr>\u003Cbr>M\u003Cbr>\u003Cbr>\u003Cbr>86 + 2b\u003Cbr>-5a + 100\u003Cbr>R\u003Cbr>\u003Cbr>\u003Cbr>130-7b\u003Cbr> L\u003Cbr>\u003Cbr>104 + 1a\u003Cbr>\u003Cbr>-4a + 157\u003Cbr>-2a + 153\u003Cbr>\u003Cbr>137-10b\u003Cbr> L\u003Cbr>\u003Cbr>5a + 88 | 2)\u003Cbr>4)\u003Cbr>6)\u003Cbr>8) |  |  |  |  |  |  |  |  |  |  |\n| 1-8 |  |  |  | 88 | 75 |  | 63 | 50 | 38 | 25 | 13 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 9)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 9)[ 9](Math www.CommonCoreSheets.com 9)  \nFinding Variable Value by Balancing Equations  \nName: Answer Key  \n\n| Find the value of 'a' and 'b'. Angle XQR is 180°. |  |  | X\u003Cbr>M\u003Cbr>Q R\u003Cbr>\u003Cbr>-5b + 53\u003Cbr>-8a + 169\u003Cbr>\u003Cbr>61-9b\u003Cbr>L\u003Cbr>\u003Cbr>-5a + 157\u003Cbr>X\u003Cbr>\u003Cbr>R\u003Cbr> 129\u003Cbr>\u003Cbr>L\u003Cbr>\u003Cbr>\u003Cbr> 139\u003Cbr>2a + 42\u003Cbr>X\u003Cbr>-8a + 152\u003Cbr> M\u003Cbr>Q\u003Cbr>\u003Cbr>86-5b\u003Cbr>R\u003Cbr>\u003Cbr>X\u003Cbr>M\u003Cbr>Q R\u003Cbr>\u003Cbr>15 + 5b\u003Cbr>-6a + 142\u003Cbr>\u003Cbr>-2b + 64\u003Cbr> L\u003Cbr>\u003Cbr>\u003Cbr>126 + 2a |  |  | Answers 1.  4   7  2.  4   2  3.  2   8  4.  7   5  5.  2   7  6.  6   2  7.  5   7  8.  2   7  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1)\u003Cbr>3)\u003Cbr>5)\u003Cbr>7) | Q\u003Cbr>X\u003Cbr>\u003Cbr>M\u003Cbr>\u003Cbr>\u003Cbr>86 + 2b\u003Cbr>-5a + 100\u003Cbr>R\u003Cbr>\u003Cbr>\u003Cbr>130-7b\u003Cbr> L\u003Cbr>\u003Cbr>104 + 1a\u003Cbr>\u003Cbr>-4a + 157\u003Cbr>-2a + 153\u003Cbr>\u003Cbr>137-10b\u003Cbr> L\u003Cbr>\u003Cbr>5a + 88 | 2)\u003Cbr>4)\u003Cbr>6)\u003Cbr>8) |  |  |  |  |  |  |  |  |  |  |\n| 1-8 |  |  |  | 88 | 75 |  | 63 | 50 | 38 | 25 | 13 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 9)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 9)[ 9](Math www.CommonCoreSheets.com 9)  \nFinding Variable Value by Balancing Equations  \nName:  \n\n| Find the value of 'a' and 'b'. Angle XQR is 180°. |  |  | X\u003Cbr>M\u003Cbr>Q R\u003Cbr>\u003Cbr>-5b + 53\u003Cbr>-8a + 169\u003Cbr>\u003Cbr>61-9b\u003Cbr>L\u003Cbr>\u003Cbr>-5a + 157\u003Cbr>X\u003Cbr>\u003Cbr>R\u003Cbr> 129\u003Cbr>\u003Cbr>L\u003Cbr>\u003Cbr>\u003Cbr> 139\u003Cbr>2a + 42\u003Cbr>\u003Cbr>92-8b\u003Cbr>128-4a\u003Cbr> L\u003Cbr>| Answers\u003Cbr>1.    \u003Cbr>2.    \u003Cbr>3.    \u003Cbr>4.    \u003Cbr>5.    \u003Cbr>6.     |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1)\u003Cbr>3)\u003Cbr>5) | Q\u003Cbr>X\u003Cbr>\u003Cbr>M\u003Cbr>\u003Cbr>\u003Cbr>86 + 2b\u003Cbr>-5a + 100\u003Cbr>R\u003Cbr>\u003Cbr>\u003Cbr>130-7b\u003Cbr> L\u003Cbr>\u003Cbr>104 + 1a\u003Cbr>\u003Cbr>-4a + 157\u003Cbr>-2a + 153 | 2)\u003Cbr>4)\u003Cbr>6) |  |  |  |  |  |  |  |\n| 1-6 |  |  |  | 83 | 67 | 50 | 33 | 17 | 0 |\n\nMath  \nModified  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n9","cbCaiuz3Eklc2hZu","https://ap.wps.com/l/cbCaiuz3Eklc2hZu","pdf",46899,"English","# Find the value of 'a' and 'b'\n## Angle XQR is 180°\n## Answer key","[{\"question\":\"How do you determine the values of a and b in these problems?\",\"answer\":\"Set up balanced equations using the given expressions and relationships, then solve the resulting linear system for a and b.\"},{\"question\":\"What role does the condition “Angle XQR is 180°” play?\",\"answer\":\"It provides the geometric constraint used to form or justify the equation relationships among the labeled parts.\"},{\"question\":\"Where are the correct answers provided?\",\"answer\":\"An “Answer Key” section lists the solved values for each numbered item.\"}]","Finding Variable Value by Balancing Equations - Worksheet | PDF",1790771568]