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Students determine which given statement must be true by using relationships among triangle interior angles, including cases where angles are equal or have specified measures (such as 75°, 70°, 50°, 40°, and 45°). Multiple-choice options ask students to compute sums like m∠1 + m∠2, m∠1 + m∠3, or m∠2 + m∠3 and select the correct result based on the required angle sum.",{"@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/using-the-angle-sum-of-a-triangle-determine-which-statement-must-be-true/466490/",{"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/using-the-angle-sum-of-a-triangle-determine-which-statement-must-be-true/466490.png","ImageObject",300,407,{"name":92,"@type":93},"Noah","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What concept is used to solve these problems?","Question",{"text":112,"@type":113},"The problems use the angle sum of the interior angles of a triangle (which totals 180°), along with given equalities or angle measures.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do you use cases where angles are equal (like m∠2 = m∠3)?",{"text":117,"@type":113},"Use the equality to set those angles equal to the given measure, then apply 180° total to find the remaining angles and compute the requested sum.",{"name":119,"@type":110,"acceptedAnswer":120},"What kinds of expressions are asked to compute?",{"text":121,"@type":113},"The worksheet repeatedly asks for angle sums such as m∠1 + m∠2, m∠1 + m∠3, or m∠2 + m∠3 and then selects the correct multiple-choice option.","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},466490,1792919245,{"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":29,"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},8796095462418,"https://ap-avatar.wpscdn.com/avatar/80000253c1241d02b47?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778826106357471780","Using the Angle Sum of a Triangle  \nName:  \n\n| Determine which statement must be true.\u003Cbr>1) In the triangle shown, m∠2 = m∠3 and m∠3 = 75° .\u003Cbr>\u003Cbr>3\u003Cbr>21\u003Cbr>A. m∠1 + m∠3 = 180°\u003Cbr>B. m∠1 + m∠3 = 105°\u003Cbr>C. m∠1 + m∠3 = 150°\u003Cbr>D. m∠1 + m∠3 = 75°\u003Cbr>3) In the triangle shown, m∠1 = m∠3 and m∠2 = 70° .\u003Cbr>\u003Cbr>A. m∠1 + m∠2 = 125°\u003Cbr>B. m∠1 + m∠2 = 180°\u003Cbr>C. m∠1 + m∠2 = 70°\u003Cbr>D. m∠1 + m∠2 = 140°\u003Cbr>5) In the triangle shown, m∠1 = m∠2 and m∠2 = 75° .\u003Cbr>\u003Cbr>A. m∠1 + m∠3 = 75°\u003Cbr>B. m∠1 + m∠3 = 105°\u003Cbr>C. m∠1 + m∠3 = 150°\u003Cbr>D. m∠1 + m∠3 = 180° | 2)\u003Cbr>4)\u003Cbr>6) | In the triangle shown, m∠1 = m∠2 and m∠3 = 50° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠1 + m∠2 = 50°\u003Cbr>B. m∠1 + m∠2 = 180°\u003Cbr>C. m∠1 + m∠2 = 100°\u003Cbr>D. m∠1 + m∠2 = 130°\u003Cbr>In the triangle shown, m∠1 = m∠3 and m∠3 = 40° .\u003Cbr>\u003Cbr>A. m∠2 + m∠3 = 80°\u003Cbr>B. m∠2 + m∠3 = 180°\u003Cbr>C. m∠2 + m∠3 = 140°\u003Cbr>D. m∠2 + m∠3 = 40°\u003Cbr>In the triangle shown, m∠1 = m∠3 and m∠3 = 45° .\u003Cbr>\u003Cbr>A. m∠1 + m∠2 = 135°\u003Cbr>B. m∠1 + m∠2 = 45°\u003Cbr>C. m∠1 + m∠2 = 180°\u003Cbr>D. m∠1 + m∠2 = 90° |  |  | Answers |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  | 1.  \u003Cbr>2.  \u003Cbr>3.  \u003Cbr>4.  \u003Cbr>5.  \u003Cbr>6.   |  |  |  |\n| 1-6 |  |  | 83 | 67 | 50 | 33 | 17 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 2)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 2)[ 2](Math www.CommonCoreSheets.com 2)  \nUsing the Angle Sum of a Triangle  \nName: Answer Key  \n\n| Determine which statement must be true.\u003Cbr>1) In the triangle shown, m∠2 = m∠3 and m∠3 = 75° .\u003Cbr>\u003Cbr>3\u003Cbr>21\u003Cbr>A. m∠1 + m∠3 = 180°\u003Cbr>B. m∠1 + m∠3 = 105°\u003Cbr>C. m∠1 + m∠3 = 150°\u003Cbr>D. m∠1 + m∠3 = 75°\u003Cbr>3) In the triangle shown, m∠1 = m∠3 and m∠2 = 70° .\u003Cbr>\u003Cbr>A. m∠1 + m∠2 = 125°\u003Cbr>B. m∠1 + m∠2 = 180°\u003Cbr>C. m∠1 + m∠2 = 70°\u003Cbr>D. m∠1 + m∠2 = 140°\u003Cbr>5) In the triangle shown, m∠1 = m∠2 and m∠2 = 75° .\u003Cbr>\u003Cbr>A. m∠1 + m∠3 = 75°\u003Cbr>B. m∠1 + m∠3 = 105°\u003Cbr>C. m∠1 + m∠3 = 150°\u003Cbr>D. m∠1 + m∠3 = 180° | 2)\u003Cbr>4)\u003Cbr>6) | In the triangle shown, m∠1 = m∠2 and m∠3 = 50° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠1 + m∠2 = 50°\u003Cbr>B. m∠1 + m∠2 = 180°\u003Cbr>C. m∠1 + m∠2 = 100°\u003Cbr>D. m∠1 + m∠2 = 130°\u003Cbr>In the triangle shown, m∠1 = m∠3 and m∠3 = 40° .\u003Cbr>\u003Cbr>A. m∠2 + m∠3 = 80°\u003Cbr>B. m∠2 + m∠3 = 180°\u003Cbr>C. m∠2 + m∠3 = 140°\u003Cbr>D. m∠2 + m∠3 = 40°\u003Cbr>In the triangle shown, m∠1 = m∠3 and m∠3 = 45° .\u003Cbr>\u003Cbr>A. m∠1 + m∠2 = 135°\u003Cbr>B. m∠1 + m∠2 = 45°\u003Cbr>C. m∠1 + m∠2 = 180°\u003Cbr>D. m∠1 + m∠2 = 90° |  |  | Answers |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  | 1.  B \u003Cbr>2.  D \u003Cbr>3.  A \u003Cbr>4.  C \u003Cbr>5.  B \u003Cbr>6.  A  |  |  |  |\n| 1-6 |  |  | 83 | 67 | 50 | 33 | 17 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 2)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 2)[ 2](Math www.CommonCoreSheets.com 2)  \nUsing the Angle Sum of a Triangle  \nName:  \n\n| Determine which statement must be true.\u003Cbr>1) In the triangle shown, m∠2 = m∠3 and m∠3 = 75° .\u003Cbr>\u003Cbr>3\u003Cbr>21\u003Cbr>A. m∠1 + m∠3 = 180°\u003Cbr>B. m∠1 + m∠3 = 105°\u003Cbr>C. m∠1 + m∠3 = 150°\u003Cbr>D. m∠1 + m∠3 = 75°\u003Cbr>3) In the triangle shown, m∠1 = m∠3 and m∠2 = 70° .\u003Cbr>\u003Cbr>A. m∠1 + m∠2 = 125°\u003Cbr>B. m∠1 + m∠2 = 180°\u003Cbr>C. m∠1 + m∠2 = 70°\u003Cbr>D. m∠1 + m∠2 = 140° | 2)\u003Cbr>4) | In the triangle shown, m∠1 = m∠2 and m∠3 = 50° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠1 + m∠2 = 50°\u003Cbr>B. m∠1 + m∠2 = 180°\u003Cbr>C. m∠1 + m∠2 = 100°\u003Cbr>D. m∠1 + m∠2 = 130°\u003Cbr>In the triangle shown, m∠1 = m∠3 and m∠3 = 40° .\u003Cbr>\u003Cbr>A. m∠2 + m∠3 = 80°\u003Cbr>B. m∠2 + m∠3 = 180°\u003Cbr>C. m∠2 + m∠3 = 140°\u003Cbr>D. m∠2 + m∠3 = 40° | Answers |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- |\n|  |  |  | 1.  \u003Cbr>2.  \u003Cbr>3.  \u003Cbr>4.   |  |  |  |\n| 1-4 |  |  | 75 | 50 | 25 | 0 |\n\nMath  \nModified  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n2","cbCaiuvQlS6mHIl3","https://ap.wps.com/l/cbCaiuvQlS6mHIl3","pdf",45975,"English","# Determine which statement must be true\n## Angle-sum scenarios with given or equal angles\n## Multiple-choice angle-sum answers","[{\"question\":\"What concept is used to solve these problems?\",\"answer\":\"The problems use the angle sum of the interior angles of a triangle (which totals 180°), along with given equalities or angle measures.\"},{\"question\":\"How do you use cases where angles are equal (like m∠2 = m∠3)?\",\"answer\":\"Use the equality to set those angles equal to the given measure, then apply 180° total to find the remaining angles and compute the requested sum.\"},{\"question\":\"What kinds of expressions are asked to compute?\",\"answer\":\"The worksheet repeatedly asks for angle sums such as m∠1 + m∠2, m∠1 + m∠3, or m∠2 + m∠3 and then selects the correct multiple-choice option.\"}]","Using the Angle Sum of a Triangle - Determine which statement must be true | PDF",1790771339]