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Each problem specifies equal-angle conditions (e.g., m∠1 equals m∠2 or m∠2 equals m∠3) along with a provided angle measure, then tests several possible sums of angles. 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Given equalities and one angle measure, the required angle sums can be determined.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are the problems structured?",{"text":117,"@type":113},"Each item states a relationship among angles (such as m∠1 = m∠2 or m∠2 = m∠3) and gives a specific angle measure, then offers multiple-choice statements about sums like m∠2 + m∠3 or m∠1 + m∠2.",{"name":119,"@type":110,"acceptedAnswer":120},"Where can the correct answers be found?",{"text":121,"@type":113},"The document includes an “Answer Key” section listing the correct option 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},466480,1792918397,{"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},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∠1 = m∠2 and m∠3 = 40° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠2 + m∠3 = 180°\u003Cbr>B. m∠2 + m∠3 = 80°\u003Cbr>C. m∠2 + m∠3 = 110°\u003Cbr>D. m∠2 + m∠3 = 40°\u003Cbr>3) In the triangle shown, m∠1 = m∠3 and m∠2 = 40° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠1 + m∠2 = 110°\u003Cbr>B. m∠1 + m∠2 = 180°\u003Cbr>C. m∠1 + m∠2 = 40°\u003Cbr>D. m∠1 + m∠2 = 80°\u003Cbr>5) In the triangle shown, m∠1 = m∠3 and m∠3 = 70° .\u003Cbr>\u003Cbr>A. m∠1 + m∠2 = 180°\u003Cbr>B. m∠1 + m∠2 = 70°\u003Cbr>C. m∠1 + m∠2 = 110°\u003Cbr>D. m∠1 + m∠2 = 140° | 2)\u003Cbr>4)\u003Cbr>6) | In the triangle shown, m∠2 = m∠3 and m∠3 = 55° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠1 + m∠3 = 110°\u003Cbr>B. m∠1 + m∠3 = 125°\u003Cbr>C. m∠1 + m∠3 = 180°\u003Cbr>D. m∠1 + m∠3 = 55°\u003Cbr>In the triangle shown, m∠2 = m∠3 and m∠1 = 70° .\u003Cbr>\u003Cbr>A. m∠1 + m∠3 = 140°\u003Cbr>B. m∠1 + m∠3 = 125°\u003Cbr>C. m∠1 + m∠3 = 70°\u003Cbr>D. m∠1 + m∠3 = 180°\u003Cbr>In the triangle shown, m∠1 = m∠2 and m∠3 = 70° .\u003Cbr>\u003Cbr>A. m∠1 + m∠2 = 140°\u003Cbr>B. m∠1 + m∠2 = 180°\u003Cbr>C. m∠1 + m∠2 = 70°\u003Cbr>D. m∠1 + m∠2 = 110° |  |  | 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 1)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 1)[ 1](Math www.CommonCoreSheets.com 1)  \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∠1 = m∠2 and m∠3 = 40° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠2 + m∠3 = 180°\u003Cbr>B. m∠2 + m∠3 = 80°\u003Cbr>C. m∠2 + m∠3 = 110°\u003Cbr>D. m∠2 + m∠3 = 40°\u003Cbr>3) In the triangle shown, m∠1 = m∠3 and m∠2 = 40° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠1 + m∠2 = 110°\u003Cbr>B. m∠1 + m∠2 = 180°\u003Cbr>C. m∠1 + m∠2 = 40°\u003Cbr>D. m∠1 + m∠2 = 80°\u003Cbr>5) In the triangle shown, m∠1 = m∠3 and m∠3 = 70° .\u003Cbr>\u003Cbr>A. m∠1 + m∠2 = 180°\u003Cbr>B. m∠1 + m∠2 = 70°\u003Cbr>C. m∠1 + m∠2 = 110°\u003Cbr>D. m∠1 + m∠2 = 140° | 2)\u003Cbr>4)\u003Cbr>6) | In the triangle shown, m∠2 = m∠3 and m∠3 = 55° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠1 + m∠3 = 110°\u003Cbr>B. m∠1 + m∠3 = 125°\u003Cbr>C. m∠1 + m∠3 = 180°\u003Cbr>D. m∠1 + m∠3 = 55°\u003Cbr>In the triangle shown, m∠2 = m∠3 and m∠1 = 70° .\u003Cbr>\u003Cbr>A. m∠1 + m∠3 = 140°\u003Cbr>B. m∠1 + m∠3 = 125°\u003Cbr>C. m∠1 + m∠3 = 70°\u003Cbr>D. m∠1 + m∠3 = 180°\u003Cbr>In the triangle shown, m∠1 = m∠2 and m∠3 = 70° .\u003Cbr>\u003Cbr>A. m∠1 + m∠2 = 140°\u003Cbr>B. m∠1 + m∠2 = 180°\u003Cbr>C. m∠1 + m∠2 = 70°\u003Cbr>D. m∠1 + m∠2 = 110° |  |  | Answers |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  | 1.  C \u003Cbr>2.  B \u003Cbr>3.  A \u003Cbr>4.  B \u003Cbr>5.  C \u003Cbr>6.  D  |  |  |  |\n| 1-6 |  |  | 83 | 67 | 50 | 33 | 17 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 1)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 1)[ 1](Math www.CommonCoreSheets.com 1)  \nUsing the Angle Sum of a Triangle  \nName:  \n\n| Determine which statement must be true.\u003Cbr>1) In the triangle shown, m∠1 = m∠2 and m∠3 = 40° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠2 + m∠3 = 180°\u003Cbr>B. m∠2 + m∠3 = 80°\u003Cbr>C. m∠2 + m∠3 = 110°\u003Cbr>D. m∠2 + m∠3 = 40°\u003Cbr>3) In the triangle shown, m∠1 = m∠3 and m∠2 = 40° .\u003Cbr>\u003Cbr>A. m∠1 + m∠2 = 110°\u003Cbr>B. m∠1 + m∠2 = 180°\u003Cbr>C. m∠1 + m∠2 = 40°\u003Cbr>D. m∠1 + m∠2 = 80° | 2) In the triangle shown, m∠2 = m∠3 and m∠3 = 55° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠1 + m∠3 = 110°\u003Cbr>B. m∠1 + m∠3 = 125°\u003Cbr>C. m∠1 + m∠3 = 180°\u003Cbr>D. m∠1 + m∠3 = 55°\u003Cbr>4) In the triangle shown, m∠2 = m∠3 and m∠1 = 70° .\u003Cbr>\u003Cbr>A. m∠1 + m∠3 = 140°\u003Cbr>B. m∠1 + m∠3 = 125°\u003Cbr>C. m∠1 + m∠3 = 70°\u003Cbr>D. m∠1 + m∠3 = 180° | 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)  \n1","cbCaiaSzn5cddVsC","https://ap.wps.com/l/cbCaiaSzn5cddVsC","pdf",44930,"English","# Determine which statement must be true\n## Problems with given angle relationships\n## Answer key","[{\"question\":\"What is the key idea behind the angle sum questions in this worksheet?\",\"answer\":\"The problems use the triangle angle-sum principle: the interior angles of a triangle add up to 180°. Given equalities and one angle measure, the required angle sums can be determined.\"},{\"question\":\"How are the problems structured?\",\"answer\":\"Each item states a relationship among angles (such as m∠1 = m∠2 or m∠2 = m∠3) and gives a specific angle measure, then offers multiple-choice statements about sums like m∠2 + m∠3 or m∠1 + m∠2.\"},{\"question\":\"Where can the correct answers be found?\",\"answer\":\"The document includes an “Answer Key” section listing the correct option for each numbered problem.\"}]","Using the Angle Sum of a Triangle | PDF",1790771322]