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### Grade 6 - Mathematics9.18 Triangle Sum Theorem

 "The sum of the measures of the angles of a triangle is 180°". In ABC, mÐA + mÐb + mÐc = 1800 In the above triangle the sum of three angles is: 70 + 60 + 50 = 1800 Examples: In ABC, ÐA = 80° and ÐB = 70°, find ÐC = ? Solution: ÐA + ÐB = 80° + 70° = 150°. But Ð A + ÐB + ÐC = 180°. Therefore, ÐC = 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, ÐA = 70°, ÐB = 30°, find ÐC.90°60°80°70° Q 2: If 2x, x and 3x are the measures of the angles of a triangle, find the angles.90°, 45° and 30°90°, 30° and 60°45°, 45° and 90°60°, 30° and 90° Q 3: In ABC, ÐA = 100°, ÐB = 50°, find ÐC.70°35°30°60° Q 4: In ABC, ÐA = 85°, ÐB = 45°, find ÐC.50°60°70°45° Q 5: In ABC, ÐA = 45°, ÐB = 90°, find ÐC.45°45°60°40° Q 6: In ABC, ÐA = 30°, ÐB = 90°, find ÐC.45°70°75°60° Q 7: In ABC, ÐA = 100°, ÐB = 30°, find ÐC.70°60°45°50° Q 8: In ABCÐA = 60°, ÐB = 40°, find ÐC.80°70°60°45° Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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