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### Grade 7 - Mathematics7.7 Triangle Sum Theorem

 "The sum of the measures of the angles of a triangle is 180°". In ABC, mĐA + mĐb + mĐc = 1800 In the above triangle the sum of three angles is: 70 + 60 + 50 = 1800 Examples: In ABC, ĐA = 80° and ĐB = 70°, find ĐC = ? Solution: ĐA + ĐB = 80° + 70° = 150°. But Đ A + ĐB + ĐC = 180°. Therefore, ĐC = 180 ° - 150° = 30°. If the measures of the three angles of a triangle are x-2, x+6 and x+8, find them. The sum of the measures of the three angles x-2 + x+6 + x+8 = 3x+12. But the sum of the measures of the three angles of a triangle = 180°. Therefore, 3x+12 = 180°; 3x = 180 - 12 = 168. x = 168/3 = 56°. Therefore, x- 2 = 56-2 = 54°. Also x+6 = 56 + 6 = 62°. and x+8 = 56 + 8 = 64°. So, the measures of the angles are 54° 62° and 64°. Directions: Answer the following questions. 1) Prove triangle sum theorem. 2) Prove the corollary to the triangle sum theorem: The acute angles of a right triangles are complementary. 3) Draw the triangles with the following measures, use a protractor to measure angles : 600-600-600 triangle, 500-700-600 triangle, 400- 500- 900 triangle 300- 600- 900 triangle 450- 450- 900 triangle 200- 500- 1800 triangle 1200- 200- 400 triangle 1400- 100- 300 triangle 1600- 100- 100 triangle 4) Draw 5 triangles and measure the interior angles using a protractor and prove that the sum of the measures is 180 degrees.
 Q 1: In ABC, ĐA = 85°, ĐB = 45°, find ĐC.60°70°45°50° Q 2: If in ABC, ĐA = 90°, ĐB = 45°, then ĐC = ______.45°60°70°50° Q 3: In ABC, ĐA = 70°, ĐB = 30°, find ĐC.60°70°80°90° Q 4: If 2x, x and 3x are the measures of the angles of a triangle, find the angles.45°, 45° and 90°60°, 30° and 90°90°, 30° and 60°90°, 45° and 30° Q 5: In ABC, ĐA = 100°, ĐB = 50°, find ĐC.70°30°60°35° Q 6: In ABC, ĐA = 80°, ĐB = 60,°, find ĐC.40°70°45°60° Q 7: In ABCĐA = 60°, ĐB = 40°, find ĐC.80°45°70°60° Q 8: In ABC, ĐA = 30°, ĐB = 90°, find ĐC.60°70°45°75° Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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