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Students determine which option must be true by using properties of triangle angle sums together with given equal-angle conditions, such as m∠2 = m∠3, m∠1 = m∠2, or m∠1 = m∠3. Each item asks for a specific sum of angle measures (m∠1 + m∠3 or m∠1 + m∠2) matching a single correct choice. 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Using the triangle angle sum, you compute the required angle sum and match it to the correct option.",{"name":119,"@type":110,"acceptedAnswer":120},"Where are the correct answers provided?",{"text":121,"@type":113},"An answer key section lists the correct choices for the numbered problems.","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},466485,1792919246,{"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":81,"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 = 65° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠1 + m∠3 = 65°\u003Cbr>B. m∠1 + m∠3 = 115°\u003Cbr>C. m∠1 + m∠3 = 180°\u003Cbr>D. m∠1 + m∠3 = 130°\u003Cbr>3) In the triangle shown, m∠1 = m∠2 and m∠3 = 100° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠1 + m∠3 = 80°\u003Cbr>B. m∠1 + m∠3 = 180°\u003Cbr>C. m∠1 + m∠3 = 140°\u003Cbr>D. m∠1 + m∠3 = 100°\u003Cbr>5) In the triangle shown, m∠1 = m∠3 and m∠2 = 100° .\u003Cbr>\u003Cbr>A. m∠1 + m∠2 = 140°\u003Cbr>B. m∠1 + m∠2 = 100°\u003Cbr>C. m∠1 + m∠2 = 80°\u003Cbr>D. m∠1 + m∠2 = 180° | 2)\u003Cbr>4)\u003Cbr>6) | In the triangle shown, m∠1 = m∠2 and m∠2 = 55° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠2 + m∠3 = 125°\u003Cbr>B. m∠2 + m∠3 = 180°\u003Cbr>C. m∠2 + m∠3 = 55°\u003Cbr>D. m∠2 + m∠3 = 110°\u003Cbr>In the triangle shown, m∠1 = m∠3 and m∠3 = 35° .\u003Cbr>\u003Cbr>A. m∠1 + m∠2 = 35°\u003Cbr>B. m∠1 + m∠2 = 180°\u003Cbr>C. m∠1 + m∠2 = 145°\u003Cbr>D. m∠1 + m∠2 = 70°\u003Cbr>In the triangle shown, m∠1 = m∠3 and m∠2 = 50° .\u003Cbr>\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 = 115° |  |  | 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 9)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 9)[ 9](Math www.CommonCoreSheets.com 9)  \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 = 65° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠1 + m∠3 = 65°\u003Cbr>B. m∠1 + m∠3 = 115°\u003Cbr>C. m∠1 + m∠3 = 180°\u003Cbr>D. m∠1 + m∠3 = 130°\u003Cbr>3) In the triangle shown, m∠1 = m∠2 and m∠3 = 100° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠1 + m∠3 = 80°\u003Cbr>B. m∠1 + m∠3 = 180°\u003Cbr>C. m∠1 + m∠3 = 140°\u003Cbr>D. m∠1 + m∠3 = 100°\u003Cbr>5) In the triangle shown, m∠1 = m∠3 and m∠2 = 100° .\u003Cbr>\u003Cbr>A. m∠1 + m∠2 = 140°\u003Cbr>B. m∠1 + m∠2 = 100°\u003Cbr>C. m∠1 + m∠2 = 80°\u003Cbr>D. m∠1 + m∠2 = 180° | 2)\u003Cbr>4)\u003Cbr>6) | In the triangle shown, m∠1 = m∠2 and m∠2 = 55° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠2 + m∠3 = 125°\u003Cbr>B. m∠2 + m∠3 = 180°\u003Cbr>C. m∠2 + m∠3 = 55°\u003Cbr>D. m∠2 + m∠3 = 110°\u003Cbr>In the triangle shown, m∠1 = m∠3 and m∠3 = 35° .\u003Cbr>\u003Cbr>A. m∠1 + m∠2 = 35°\u003Cbr>B. m∠1 + m∠2 = 180°\u003Cbr>C. m∠1 + m∠2 = 145°\u003Cbr>D. m∠1 + m∠2 = 70°\u003Cbr>In the triangle shown, m∠1 = m∠3 and m∠2 = 50° .\u003Cbr>\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 = 115° |  |  | Answers |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  | 1.  B \u003Cbr>2.  A \u003Cbr>3.  C \u003Cbr>4.  C \u003Cbr>5.  A \u003Cbr>6.  D  |  |  |  |\n| 1-6 |  |  | 83 | 67 | 50 | 33 | 17 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 9)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 9)[ 9](Math www.CommonCoreSheets.com 9)  \nUsing the Angle Sum of a Triangle  \nName:  \n\n| Determine which statement must be true. | In the triangle shown, m∠1 = m∠2 and | Answers |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |\n| 1) In the triangle shown, m∠2 = m∠3 and m∠3 2) |  |  |  |  |  |\n| = 65° .\u003Cbr>\u003Cbr>A. m∠1 + m∠3 = 65° | m∠2 = 55° .\u003Cbr>\u003Cbr>A. m∠2 + m∠3 = 125° | 1.  \u003Cbr>2.  \u003Cbr>3.   |  |  |  |\n| B. m∠1 + m∠3 = 115°\u003Cbr>C. m∠1 + m∠3 = 180° | B. m∠2 + m∠3 = 180°\u003Cbr>C. m∠2 + m∠3 = 55° | 4.   |  |  |  |\n| D. m∠1 + m∠3 = 130° | D. m∠2 + m∠3 = 110° |  |  |  |  |\n| 3) In the triangle shown, m∠1 = m∠2 and m∠3 4) | In the triangle shown, m∠1 = m∠3 and |  |  |  |  |\n| = 100° . | m∠3 = 35° . |  |  |  |  |\n| \u003Cbr>3\u003Cbr>1 2 | \u003Cbr>3\u003Cbr>2  1  |  |  |  |  |\n| A. m∠1 + m∠3 = 80° | A. m∠1 + m∠2 = 35° |  |  |  |  |\n| B. m∠1 + m∠3 = 180° | B. m∠1 + m∠2 = 180° |  |  |  |  |\n| C. m∠1 + m∠3 = 140° | C. m∠1 + m∠2 = 145° |  |  |  |  |\n| D. m∠1 + m∠3 = 100° | D. m∠1 + m∠2 = 70° |  |  |  |  |\n| 1-4 |  | 75 | 50 | 25 | 0 |\n\nMath  \nModified  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n9","cbCaia4uwbV1RvL0","https://ap.wps.com/l/cbCaia4uwbV1RvL0","pdf",46039,"English","# Determine which statement must be true\n## Angle-sum multiple-choice problems\n## Answer key","[{\"question\":\"What does each problem ask you to find in the triangle diagrams?\",\"answer\":\"Each problem asks you to determine which statement must be true by selecting the correct value for an angle sum such as m∠1 + m∠3 or m∠1 + m∠2 from the multiple-choice options.\"},{\"question\":\"How are the given angle relationships used?\",\"answer\":\"The problems provide relationships like m∠2 = m∠3 or equal angles such as m∠1 = m∠2, along with a specific angle measure (e.g., 65°, 100°, 55°). Using the triangle angle sum, you compute the required angle sum and match it to the correct option.\"},{\"question\":\"Where are the correct answers provided?\",\"answer\":\"An answer key section lists the correct choices for the numbered problems.\"}]","Using the Angle Sum of a Triangle - Determine which statement must be true | PDF",1790771332]