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Students find the values of variables a and b from linear expressions shown for angles around points labeled L, M, X, Q, R. The prompt specifies that angle XQR is 180°, and each diagram pairs expressions for the same angle measure. The document provides multiple numbered cases and a compiled answers section listing each solution set.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/finding-variable-value-by-balancing-equations/466616/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/finding-variable-value-by-balancing-equations/466616.png","ImageObject",300,407,{"name":92,"@type":93},"Liam","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What variables must be solved in this worksheet?","Question",{"text":112,"@type":113},"The worksheet asks students to find the values of variables 'a' and 'b' from the given angle equations.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How is the angle condition used?",{"text":117,"@type":113},"It specifies that angle XQR is 180°, so the paired expressions can be balanced to determine a and b.",{"name":119,"@type":110,"acceptedAnswer":120},"Is an answer key included?",{"text":121,"@type":113},"Yes. The document contains an answers section that lists the final values for each numbered problem.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},466616,1792856344,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":39},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°. |  |  | \u003Cbr>\u003Cbr>44-4b 32 + 2b\u003Cbr>-1a + 150 1a + 138\u003Cbr>\u003Cbr>M\u003Cbr>X Q\u003Cbr>\u003Cbr> 134\u003Cbr>142-9a\u003Cbr>R\u003Cbr>\u003Cbr>\u003Cbr>M\u003Cbr>X Q\u003Cbr>\u003Cbr>-10a + 106\u003Cbr>R\u003Cbr>-2b + 122\u003Cbr>\u003Cbr>M\u003Cbr>\u003Cbr>X Q\u003Cbr>\u003Cbr>-4b + 170\u003Cbr>102-6a\u003Cbr>R\u003Cbr>\u003Cbr>-10b + 218\u003Cbr>L\u003Cbr>\u003Cbr>-1a + 52 |  |  | Answers\u003Cbr>1.    \u003Cbr>2.    \u003Cbr>3.    \u003Cbr>4.    \u003Cbr>5.    \u003Cbr>6.    \u003Cbr>7.    \u003Cbr>8.     |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1) | | 2) |  |  |  |  |  |  |  |  |  |  |\n| 3)\u003Cbr>\u003Cbr>\u003Cbr>4)\u003Cbr>-2b + 50 3b + 5\u003Cbr>183-5a\u003Cbr>162-2a |  |  |  |  |  |  |  |  |  |  |  |  |\n| 5)\u003Cbr>7) | M\u003Cbr>\u003Cbr>X Q\u003Cbr>\u003Cbr>-1b + 145\u003Cbr>119-11a\u003Cbr>R\u003Cbr>\u003Cbr>208-10b\u003Cbr>L\u003Cbr>\u003Cbr>70-4a\u003Cbr>\u003Cbr>M\u003Cbr>X Q\u003Cbr>\u003Cbr> 119\u003Cbr>1a + 49\u003Cbr>R\u003Cbr>\u003Cbr>L\u003Cbr>\u003Cbr>\u003Cbr>131-3b\u003Cbr>4a + 31 | 6)\u003Cbr>8) |  |  |  |  |  |  |  |  |  |  |\n| 1-8 |  |  |  | 88 | 75 |  | 63 | 50 | 38 | 25 | 13 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 4)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 4)[ 4](Math www.CommonCoreSheets.com 4)  \nFinding Variable Value by Balancing Equations  \nName: Answer Key  \n\n| Find the value of 'a' and 'b'. Angle XQR is 180°. |  |  | \u003Cbr>\u003Cbr>L\u003Cbr>\u003Cbr>M\u003Cbr>X\u003Cbr>142-9a\u003Cbr>Q\u003Cbr> 134\u003Cbr>1a + 138\u003Cbr>R\u003Cbr>\u003Cbr>L\u003Cbr>\u003Cbr>102-5a\u003Cbr>\u003Cbr>M\u003Cbr>X Q\u003Cbr>\u003Cbr>-10a + 106\u003Cbr>R\u003Cbr>-2b + 122\u003Cbr>\u003Cbr>M\u003Cbr>\u003Cbr>X Q\u003Cbr>\u003Cbr>-4b + 170\u003Cbr>102-6a\u003Cbr>R\u003Cbr>\u003Cbr>-10b + 218\u003Cbr>L\u003Cbr>\u003Cbr>-1a + 52 |  |  | Answers 1.  4   3  2.  6   2  3.  7   9  4.  10   3  5.  7   7  6.  3   9  7.  6   2  8.  10   8  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1)\u003Cbr>3)\u003Cbr>5)\u003Cbr>7) | \u003Cbr>M\u003Cbr>X Q\u003Cbr>\u003Cbr>-8a + 96\u003Cbr>R\u003Cbr>101 \u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>L\u003Cbr>M\u003Cbr>\u003Cbr>X\u003Cbr>\u003Cbr>119-11a\u003Cbr>208-10b\u003Cbr>L\u003Cbr>\u003Cbr>R\u003Cbr>\u003Cbr>4a + 31 | 2)\u003Cbr>4)\u003Cbr>6)\u003Cbr>8) |  |  |  |  |  |  |  |  |  |\n| L\u003Cbr>|  |  |  |  |  |  |  |  |  |  |  |\n| 1-8 |  |  |  | 88 | 75 | 63 | 50 | 38 | 25 | 13 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 4)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 4)[ 4](Math www.CommonCoreSheets.com 4)  \nFinding Variable Value by Balancing Equations  \nName:  \n\n| Find the value of 'a' and 'b'. Angle XQR is 180°. |  |  | \u003Cbr>\u003Cbr>44-4b 32 + 2b\u003Cbr>-1a + 150 1a + 138\u003Cbr>\u003Cbr>M\u003Cbr>X Q\u003Cbr>\u003Cbr> 134\u003Cbr>142-9a\u003Cbr>R\u003Cbr>\u003Cbr>\u003Cbr>-10b + 194\u003Cbr>L\u003Cbr>\u003Cbr>\u003Cbr>-4a + 88 | Answers\u003Cbr>1.    \u003Cbr>2.    \u003Cbr>3.    \u003Cbr>4.    \u003Cbr>5.    \u003Cbr>6.     |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1) | | 2) |  |  |  |  |  |  |  |\n| 3)\u003Cbr>\u003Cbr>\u003Cbr>4)\u003Cbr>-2b + 50 3b + 5\u003Cbr>183-5a\u003Cbr>162-2a |  |  |  |  |  |  |  |  |  |\n| 5)\u003Cbr>M\u003Cbr>\u003Cbr>X Q\u003Cbr>\u003Cbr>-1b + 145\u003Cbr>119-11a\u003Cbr>R\u003Cbr>\u003Cbr>208-10b\u003Cbr>L\u003Cbr>\u003Cbr>70-4a |  | 6) |  |  |  |  |  |  |  |\n| 1-6 |  |  |  | 83 | 67 | 50 | 33 | 17 | 0 |\n\nMath  \nModified  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n4","cbCainwM1okBiVwO","https://ap.wps.com/l/cbCainwM1okBiVwO","pdf",46903,"English","# Find the value of 'a' and 'b'\n## Angle XQR is 180°\n## Answer key","[{\"question\":\"What variables must be solved in this worksheet?\",\"answer\":\"The worksheet asks students to find the values of variables 'a' and 'b' from the given angle equations.\"},{\"question\":\"How is the angle condition used?\",\"answer\":\"It specifies that angle XQR is 180°, so the paired expressions can be balanced to determine a and b.\"},{\"question\":\"Is an answer key included?\",\"answer\":\"Yes. The document contains an answers section that lists the final values for each numbered problem.\"}]","Finding Variable Value by Balancing Equations | PDF",1790771584]