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m∠2 = m∠3 and m∠3 = 70° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠1 + m∠2 = 180°\u003Cbr>B. m∠1 + m∠2 = 140°\u003Cbr>C. m∠1 + m∠2 = 110°\u003Cbr>D. m∠1 + m∠2 = 70°\u003Cbr>3) In the triangle shown, m∠1 = m∠3 and m∠3 = 50° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠2 + m∠3 = 180°\u003Cbr>B. m∠2 + m∠3 = 100°\u003Cbr>C. m∠2 + m∠3 = 50°\u003Cbr>D. m∠2 + m∠3 = 130°\u003Cbr>5) In the triangle shown, m∠2 = m∠3 and m∠1 = 80° .\u003Cbr>\u003Cbr>A. m∠2 + m∠3 = 100°\u003Cbr>B. m∠2 + m∠3 = 80°\u003Cbr>C. m∠2 + m∠3 = 160°\u003Cbr>D. m∠2 + m∠3 = 180° | 2)\u003Cbr>4)\u003Cbr>6) | 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 = 180°\u003Cbr>D. m∠1 + m∠2 = 80°\u003Cbr>In the triangle shown, m∠1 = m∠2 and m∠2 = 75° .\u003Cbr>\u003Cbr>3\u003Cbr>12\u003Cbr>A. m∠1 + m∠3 = 150°\u003Cbr>B. m∠1 + m∠3 = 180°\u003Cbr>C. m∠1 + m∠3 = 75°\u003Cbr>D. m∠1 + m∠3 = 105°\u003Cbr>In the triangle shown, m∠1 = m∠3 and m∠2 = 40° .\u003Cbr>\u003Cbr>A. m∠2 + m∠3 = 80°\u003Cbr>B. m∠2 + m∠3 = 180°\u003Cbr>C. m∠2 + m∠3 = 110°\u003Cbr>D. m∠2 + m∠3 = 40° |  |  | 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 4)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 4)[ 4](Math www.CommonCoreSheets.com 4)  \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 = 70° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠1 + m∠2 = 180°\u003Cbr>B. m∠1 + m∠2 = 140°\u003Cbr>C. m∠1 + m∠2 = 110°\u003Cbr>D. m∠1 + m∠2 = 70°\u003Cbr>3) In the triangle shown, m∠1 = m∠3 and m∠3 = 50° .\u003Cbr>\u003Cbr>3\u003Cbr>1 2\u003Cbr>A. m∠2 + m∠3 = 180°\u003Cbr>B. m∠2 + m∠3 = 100°\u003Cbr>C. m∠2 + m∠3 = 50°\u003Cbr>D. m∠2 + m∠3 = 130°\u003Cbr>5) In the triangle shown, m∠2 = m∠3 and m∠1 = 80° .\u003Cbr>\u003Cbr>A. m∠2 + m∠3 = 100°\u003Cbr>B. m∠2 + m∠3 = 80°\u003Cbr>C. m∠2 + m∠3 = 160°\u003Cbr>D. m∠2 + m∠3 = 180° | 2)\u003Cbr>4)\u003Cbr>6) | 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 = 180°\u003Cbr>D. m∠1 + m∠2 = 80°\u003Cbr>In the triangle shown, m∠1 = m∠2 and m∠2 = 75° .\u003Cbr>\u003Cbr>3\u003Cbr>12\u003Cbr>A. m∠1 + m∠3 = 150°\u003Cbr>B. m∠1 + m∠3 = 180°\u003Cbr>C. m∠1 + m∠3 = 75°\u003Cbr>D. m∠1 + m∠3 = 105°\u003Cbr>In the triangle shown, m∠1 = m∠3 and m∠2 = 40° .\u003Cbr>\u003Cbr>A. m∠2 + m∠3 = 80°\u003Cbr>B. m∠2 + m∠3 = 180°\u003Cbr>C. m∠2 + m∠3 = 110°\u003Cbr>D. m∠2 + m∠3 = 40° |  |  | Answers |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  | 1.  C \u003Cbr>2.  A \u003Cbr>3.  D \u003Cbr>4.  D \u003Cbr>5.  A \u003Cbr>6.  C  |  |  |  |\n| 1-6 |  |  | 83 | 67 | 50 | 33 | 17 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 4)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 4)[ 4](Math www.CommonCoreSheets.com 4)  \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 2) In the triangle shown, m∠1 = m∠3 and\u003Cbr>= 70° . m∠2 = 100° . |  | Answers |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n|  |  | 1.  \u003Cbr>2.  \u003Cbr>3.  \u003Cbr>4.   |  |  |  |\n| \u003Cbr>A. m∠1 + m∠2 = 180°\u003Cbr>B. m∠1 + m∠2 = 140°\u003Cbr>C. m∠1 + m∠2 = 110°\u003Cbr>D. m∠1 + m∠2 = 70° | \u003Cbr>A. m∠1 + m∠2 = 140°\u003Cbr>B. m∠1 + m∠2 = 100°\u003Cbr>C. m∠1 + m∠2 = 180°\u003Cbr>D. m∠1 + m∠2 = 80° |  |  |  |  |\n| 3) In the triangle shown, m∠1 = m∠3 and m∠3 4) In the triangle shown, m∠1 = m∠2 and = 50° . m∠2 = 75° . |  |  |  |  |  |\n| \u003Cbr>A. m∠2 + m∠3 = 180°\u003Cbr>B. m∠2 + m∠3 = 100°\u003Cbr>C. m∠2 + m∠3 = 50°\u003Cbr>D. m∠2 + m∠3 = 130° | \u003Cbr>A. m∠1 + m∠3 = 150°\u003Cbr>B. m∠1 + m∠3 = 180°\u003Cbr>C. m∠1 + m∠3 = 75°\u003Cbr>D. m∠1 + m∠3 = 105° |  |  |  |  |\n| 1-4 |  | 75 | 50 | 25 | 0 |\n\nMath  \nModified  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n4","cbCaidR8Oh52P9jq","https://ap.wps.com/l/cbCaidR8Oh52P9jq","pdf",45856,"English","# Determine which statement must be true\n## Angle-sum equation options for each triangle problem\n## Answer key selections","[{\"question\":\"What principle do these problems use to find the correct statement?\",\"answer\":\"They use the triangle interior angle sum, where the three angles add up to 180°.\"},{\"question\":\"How are the problems constructed?\",\"answer\":\"Each problem provides relationships like m∠2 = m∠3 (or m∠1 = m∠3, etc.) plus a given angle measure, then asks which sum equation must be true.\"},{\"question\":\"Where can the correct answers be found?\",\"answer\":\"The provided answer key lists the selected option (A–D) for each numbered problem.\"}]","Using the Angle Sum of a Triangle - Determine which statement must be true | PDF",1790771345]