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Mastering Angles in Triangles Course 3

Learn to solve triangle angle equations, identify triangle types, and apply the Triangle Sum Theorem. Discover properties of acute, right, obtuse, equilateral, isosceles, and scalene triangles. Practice finding unknown angle measures with detailed examples and explanations.

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Mastering Angles in Triangles Course 3

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  1. 7-3 Angles in Triangles Warm Up Problem of the Day Lesson Presentation Course 3

  2. 7-3 Angles in Triangles Course 3 Warm Up Solve each equation. 1. 62 + x + 37 = 180 2. x + 90 + 11 = 180 3. 2x + 18 = 180 4. 180 = 2x + 72 + x x = 81 x = 79 x = 81 x = 36

  3. 7-3 Angles in Triangles Course 3 Problem of the Day What is the one hundred fiftieth day of a non-leap year? May 30

  4. 7-3 Angles in Triangles Course 3 Learn to find unknown angles in triangles.

  5. 7-3 Angles in Triangles Course 3 Insert Lesson Title Here Vocabulary Triangle Sum Theorem acute triangle right triangle obtuse triangle equilateral triangle isosceles triangle scalene triangle

  6. 7-3 Angles in Triangles Course 3 If you tear off two corners of a triangle and place them next to the third corner, the three angles seem to form a straight line.

  7. 7-3 Angles in Triangles Course 3 Draw a triangle and extend one side. Then draw a line parallel to the extended side, as shown. The sides of the triangle are transversals to the parallel lines. The three angles in the triangle can be arranged to form a straight line or 180°.

  8. 7-3 Angles in Triangles Course 3 An acute triangle has 3 acute angles. A right triangle has 1 right angle. An obtuse triangle has 1 obtuse angle.

  9. 7-3 Angles in Triangles –117° –117° Course 3 Additional Example 1A: Finding Angles in Acute, Right and Obtuse Triangles Find p° in the acute triangle. 73° + 44° + p° = 180° 117° + p° = 180° p° = 63°

  10. 7-3 Angles in Triangles –132° –132° Course 3 Additional Example 1B: Finding Angles in Acute, Right, and Obtuse Triangles Find c° in the right triangle. 42° + 90° + c° = 180° 132° + c° = 180° c° = 48°

  11. 7-3 Angles in Triangles –85° –85° Course 3 Additional Example 1C: Finding Angles in Acute, Right, and Obtuse Triangles Find m° in the obtuse triangle. 23° + 62° + m° = 180° 85° + m° = 180° m° = 95°

  12. 7-3 Angles in Triangles –126° –126° Course 3 Check It Out: Example 1A Find a° in the acute triangle. 88° + 38° + a° = 180° 38° 126° + a° = 180° a° = 54° 88° a°

  13. 7-3 Angles in Triangles –128° –128° Course 3 Check It Out: Example 1B Find b in the right triangle. 38° 38° + 90° + b° = 180° 128° + b° = 180° b° = 52° b°

  14. 7-3 Angles in Triangles –62° –62° Course 3 Check It Out: Example 1C Find c° in the obtuse triangle. 24° + 38° + c° = 180° 38° 62° + c° = 180° 24° c° c° = 118°

  15. 7-3 Angles in Triangles Course 3 An equilateral triangle has 3 congruent sides and 3 congruent angles. An isosceles triangle has at least 2 congruent sides and 2 congruent angles. A scalene triangle has no congruent sides and no congruent angles.

  16. 7-3 Angles in Triangles 3b° 180° = 3 3 Course 3 Additional Example 2A: Finding Angles in Equilateral, Isosceles, and Scalene Triangles Find the angle measures in the equilateral triangle. 3b° = 180° Triangle Sum Theorem Divide both sides by 3. b° = 60° All three angles measure 60°.

  17. 7-3 Angles in Triangles –62° –62° 2t° = 118° 2 2 Course 3 Additional Example 2B: Finding Angles in Equilateral, Isosceles, and Scalene Triangles Find the angle measures in the isosceles triangle. 62° + t° + t° = 180° Triangle Sum Theorem Combine like terms. 62° + 2t° = 180° Subtract 62° from both sides. 2t° = 118° Divide both sides by 2. t° = 59° The angles labeled t° measure 59°.

  18. 7-3 Angles in Triangles 10 10 Course 3 Additional Example 2C: Finding Angles in Equilateral, Isosceles, and Scalene Triangles Find the angle measures in the scalene triangle. 2x° + 3x° + 5x° = 180° Triangle Sum Theorem Combine like terms. 10x° = 180° Divide both sides by 10. x = 18° The angle labeled 2x° measures 2(18°) = 36°, the angle labeled 3x° measures 3(18°) = 54°, and the angle labeled 5x° measures 5(18°) = 90°.

  19. 7-3 Angles in Triangles –39° –39° 2t° = 141° 2 2 Course 3 Check It Out: Example 2A Find the angle measures in the isosceles triangle. 39° + t° + t° = 180° Triangle Sum Theorem Combine like terms. 39° + 2t° = 180° Subtract 39° from both sides. 2t° = 141° Divide both sides by 2 39° t° = 70.5° t° The angles labeled t° measure 70.5°. t°

  20. 7-3 Angles in Triangles 20 20 Course 3 Check It Out: Example 2B Find the angle measures in the scalene triangle. 3x° + 7x° + 10x° = 180° Triangle Sum Theorem 20x° = 180° Combine like terms. Divide both sides by 20. x = 9° 10x° The angle labeled 3x° measures 3(9°) = 27°, the angle labeled 7x° measures 7(9°) = 63°, and the angle labeled 10x° measures 10(9°) = 90°. 3x° 7x°

  21. 7-3 Angles in Triangles 3x° 180° = 3 3 Course 3 Check It Out: Example 2C Find the angle measures in the equilateral triangle. 3x° = 180° Triangle Sum Theorem x° x° = 60° x° x° All three angles measure 60°.

  22. 7-3 Angles in Triangles Let x° = the first angle measure. Then 6x° = second angle measure, and (6x°) = 3x° = third angle measure. 12 Course 3 Additional Example 3: Finding Angles in a Triangle that Meets Given Conditions The second angle in a triangle is six times as large as the first. The third angle is half as large as the second. Find the angle measures and draw a possible picture.

  23. 7-3 Angles in Triangles 10 10 Let x° = the first angle measure. Then 6x° = second angle measure, and (6x°) = 3x° = third angle. 12 Course 3 Additional Example 3 Continued Triangle Sum Theorem x° + 6x° + 3x° = 180° Combine like terms. 10x° = 180° Divide both sides by 10. x° = 18°

  24. 7-3 Angles in Triangles Let x° = the first angle measure. Then 6x° = second angle measure, and (6x°) = 3x° = third angle. 12 Course 3 Additional Example 3 Continued The angles measure 18°, 54°, and 108°. The triangle is an obtuse scalene triangle. x° = 18° 3 • 18° = 54° 6 • 18° = 108° X° = 18°

  25. 7-3 Angles in Triangles Let x° = the first angle measure. Then 3x° = second angle measure, and (3x°) = x° = third angle measures. 13 Course 3 Check It Out: Example 3 The second angle in a triangle is three times larger than the first. The third angle is one third as large as the second. Find the angle measures and draw a possible picture.

  26. 7-3 Angles in Triangles 5 5 Let x° = the first angle measure. Then 3x° = second angle measure, and (3x°) = 3x° = third angle. 13 Course 3 Check It Out: Example 3 Continued Triangle Sum Theorem x° + 3x° + x° = 180° Combine like terms. 5x° = 180° Divide both sides by 5. x° = 36°

  27. 7-3 Angles in Triangles Let x° = the first angle measure. Then 3x° = second angle measure, and (3x°) = x° = third angle. 108° 13 36° 36° Course 3 Check It Out: Example 3 Continued The angles measure 36°, 36°, and 108°. The triangle is an obtuse isosceles triangle. x° = 36° 3 • 36° = 108° x° = 36°

  28. 7-3 Angles in Triangles Course 3 Lesson Quiz: Part I 1. Find the missing angle measure in the acute triangle shown. 38° 2. Find the missing angle measure in the right triangle shown. 55°

  29. 7-3 Angles in Triangles Course 3 Lesson Quiz: Part II 3. Find the missing angle measure in an acute triangle with angle measures of 67° and 63°. 50° 4. Find the missing angle measure in an obtuse triangle with angle measures of 10° and 15°. 155°

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