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An accompanying answer key provides the computed angle values for problems 1 through 6.",{"@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/adding-a-ray-and-calculating-angle-solve-each-problem-and-find-angle-measures/467787/",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/adding-a-ray-and-calculating-angle-solve-each-problem-and-find-angle-measures/467787.png","ImageObject",300,407,{"name":42,"@type":43},"Theodore","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",7,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What does it mean to add a ray BD in these problems?","Question",{"text":63,"@type":64},"You draw and label ray BD so that it cuts angle ABC into two smaller angles.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you find the missing angle measure?",{"text":68,"@type":64},"Use the given angle value (either ∠DBC or ∠ABD) and the fact that BD splits ∠ABC into two parts, then compute the other angle.",{"name":70,"@type":61,"acceptedAnswer":71},"Where can the correct answers be checked?",{"text":72,"@type":64},"The document includes an answer key listing the angle measures for problems 1 through 6.","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},467787,1792917249,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,109,114,119,122,126],{"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":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},"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":96,"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},7971461740886,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","Adding a Ray and Calculating Angle  \nName:  \n\n| Solve each problem. 1)\u003Cbr>153°\u003Cbr>C\u003Cbr>\u003Cbr>B\u003Cbr>A\u003Cbr>A. Draw and label ray BD so that it cuts angle ABC into two smaller angles, with angle DBC measuring 90 degrees.\u003Cbr>B. What is the measure of angle ABD?\u003Cbr>3)\u003Cbr>C\u003Cbr>\u003Cbr>\u003Cbr>61°\u003Cbr>B\u003Cbr>A\u003Cbr>A. Draw and label ray BD so that it cuts angle ABC into two smaller angles, with angle ABD measuring 30 degrees.\u003Cbr>B. What is the measure of angle DBC?\u003Cbr>5)\u003Cbr>164°\u003Cbr>\u003Cbr>A\u003Cbr>A. Draw and label ray BD so that it cuts angle ABC into two smaller angles, with angle DBC measuring 70 degrees.\u003Cbr>B. What is the measure of angle ABD? | 2)\u003Cbr>4)\u003Cbr>6) | C\u003Cbr>\u003Cbr>B\u003Cbr>A\u003Cbr>A. Draw and label ray BD so that it cuts angle ABC into two smaller angles, with angle DBC measuring 78 degrees.\u003Cbr>B. What is the measure of angle ABD?\u003Cbr>C\u003Cbr>\u003Cbr>B\u003Cbr>A\u003Cbr>A. Draw and label ray BD so that it cuts angle ABC into two smaller angles, with angle DBC measuring 49 degrees.\u003Cbr>B. What is the measure of angle ABD?\u003Cbr>\u003Cbr>B\u003Cbr>A\u003Cbr>A. Draw and label ray BD so that it cuts angle ABC into two smaller angles, with angle ABD measuring 43 degrees.\u003Cbr>B. What is the measure of angle DBC? | 1.\u003Cbr>2.\u003Cbr>3.\u003Cbr>4.\u003Cbr>5.\u003Cbr>6. |  | Answers |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |\n| 1-6 |  |  | 83 | 67 |  | 50 | 33 | 17 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 7)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 7)[ 7](Math www.CommonCoreSheets.com 7)  \nAdding a Ray and Calculating Angle  \nName: Answer Key  \n\n| Solve each problem. |  |  |  |  | 2)\u003Cbr>4)\u003Cbr>6) | C\u003Cbr>\u003Cbr>D\u003Cbr>B |  | A |  | Answers 1.  63°  2.  39°  3.  31°  4.  65°  5.  94°  6.  86°  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1)\u003Cbr>3)\u003Cbr>5) | C | \u003Cbr>\u003Cbr>90\u003Cbr>153°\u003Cbr>\u003Cbr>D\u003Cbr>\u003Cbr>63\u003Cbr>\u003Cbr>B | A |  |  |  |  |  |  |  |  |  |  |  |  |\n|  | A. Draw and label ray BD so that it cuts angle ABC into two smaller angles, with angle DBC measuring 90 degrees.\u003Cbr>B. What is the measure of angle ABD?\u003Cbr>C\u003Cbr>\u003Cbr>A\u003Cbr>B\u003Cbr>\u003Cbr>61°\u003Cbr>\u003Cbr>\u003Cbr>D\u003Cbr>\u003Cbr>\u003Cbr>A. Draw and label ray BD so that it cuts angle ABC into two smaller angles, with angle ABD measuring 30 degrees.\u003Cbr>B. What is the measure of angle DBC? |  |  |  |  | A. Draw and label ray BD so that it cuts angle ABC into two smaller angles, with angle DBC measuring 78 degrees.\u003Cbr>B. What is the measure of angle ABD? |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | C D\u003Cbr>\u003Cbr>B | A |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | A. Draw and label ray BD so that it cuts angle ABC into two smaller angles, with angle DBC measuring 49 degrees.\u003Cbr>B. What is the measure of angle ABD? |  |  |  |  |  |  |  |  |  |\n|  | C | D\u003Cbr>\u003Cbr>B |  | A |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | \u003Cbr>C\u003Cbr>\u003Cbr>129°\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>D\u003Cbr>B |  |  | A |  |  |  |  |  |  |\n|  | A. Draw and label ray BD so that it cuts angle ABC into two smaller angles, with angle DBC measuring 70 degrees.\u003Cbr>B. What is the measure of angle ABD? |  |  |  |  | A. Draw and label ray BD so that it cuts angle ABC into two smaller angles, with angle ABD measuring 43 degrees.\u003Cbr>B. What is the measure of angle DBC? |  |  |  |  |  |  |  |  |  |\n| 1-6 |  |  |  |  |  |  |  |  |  | 83 | 67 | 50 | 33 | 17 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 7)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 7)[ 7](Math www.CommonCoreSheets.com 7)  \nAdding a Ray and Calculating Angle  \nName:  \n\n| Solve each problem. |  |  |  |  |  |  |  |  |  | Answers |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| | 39° 31° |  |  |  | 63° 65° |  |  |  | |  |  |  |  |  |\n| 1)\u003Cbr>3) | 153° |  |  | A | 2)\u003Cbr>4) | C\u003Cbr>\u003Cbr>B |  | A |  | 1.  \u003Cbr>2.  \u003Cbr>3.  \u003Cbr>4.   |  |  |","cbCaifQKmoWYASR7","https://ap.wps.com/l/cbCaifQKmoWYASR7","pdf",52216,"English","# Solve each problem\n## Draw ray and split angle ABC\n## Find the missing angle measure\n## Use the answer key","[{\"question\":\"What does it mean to add a ray BD in these problems?\",\"answer\":\"You draw and label ray BD so that it cuts angle ABC into two smaller angles.\"},{\"question\":\"How do you find the missing angle measure?\",\"answer\":\"Use the given angle value (either ∠DBC or ∠ABD) and the fact that BD splits ∠ABC into two parts, then compute the other angle.\"},{\"question\":\"Where can the correct answers be checked?\",\"answer\":\"The document includes an answer key listing the angle measures for problems 1 through 6.\"}]","Adding a Ray and Calculating Angle - Solve each problem and find angle measures | PDF",1790773361]