? LESSON 15.2 ESSENTIL QUESTION Sum of ngle Measures in a Triangle How do you use the sum of angles in a triangle to find an unknown angle measure? Epressions, equations, and relationships 6.8. Etend previous knowledge of triangles and their properties to include the sum of angles in a triangle EXPLORE TIVITY 6.8. Eploring ngles in a Triangle Recall that a triangle is a closed figure with three line segments and three angles. The measures of the angles of a triangle have a special relationship with one another. 2 Use a straightedge to draw a large triangle. Label the angles 1, 2, and 3. 1 3 Use scissors to cut out the triangle. Tear off the three angles. rrange them around a point on a line as shown. 1 2 3 What is the measure of the straight angle formed by the three angles? E What is the sum of the measures of the three angles? Eplain. Houghton Mifflin Harcourt Publishing ompany F Reflect ompare your results with those of your classmates. What guess can you make? 1. Justify Reasoning How can you show that your guess is correct? Lesson 15.2 429
Finding an ngle Measure in a Triangle Math On the Spot Sum of ngle Measures of a Triangle The sum of the measures of the angles in a triangle is 180. 2 1 3 m 1 + m 2 + m 3 = 180 EXMPLE 1 6.8. Fountain Place, shown to the right, is a 720-foot allas skyscraper. Find the measure of the unknown angle in the triangle at the top of the building. m 1 + m 2 + m 3 = 180 65 + 65 + = 180 130 + = 180 The sum of the angle measures in a triangle is 180. Write an equation. dd. 65 65 130 130 = 50 Subtract 130 from both sides. Math Talk Mathematical Processes an a triangle have two obtuse angles? Why or why not? Personal Math Trainer Online ssessment and Intervention The angle at the top of the triangle measures 50. YOUR TURN Find the unknown angle measures. 2. 3. E 100 F 55 71 56 J = = K L Houghton Mifflin Harcourt Publishing ompany 430 Unit 5
Finding ngles in an Equilateral Triangle Recall that an equilateral triangle has three congruent sides and three congruent angles. EXMPLE 2 6.8. Math On the Spot Find the angle measures in the equilateral triangle. 3 = 180 3 3 = 180 3 = 60 Write an equation. ivide both sides by 3. Each angle in an equilateral triangle measures 60. Reflect 4. Multiple Representations Write a different equation to find the angle measures in Eample 2. Will the answer be the same? Eplain. 5. raw onclusions Triangle is a right triangle. What conclusions can you draw about the measures of the angles of the triangle? Houghton Mifflin Harcourt Publishing ompany YOUR TURN Write an equation to find the unknown angle measure in each triangle. 6. The measures of two of the angles are 25 and 65. 7. The measures of two of the angles are 60. 8. The measures of two of the angles are 35. Personal Math Trainer Online ssessment and Intervention Lesson 15.2 431
Guided Practice 1. The sum of the angle measures in a triangle is. (Eplore ctivity) Find the unknown angle measure in each triangle. (Eamples 1 and 2) 2. m R + m S + m T = + + = S 105 T + = - - R 42 = 3. K 4. 96 J 42 L 28 = = 5. G 6. 33 M 61 F 28 H P 59 N = =? 7. The measures of two of the angles are 45. 8. The measures of two of the angles are 50 and 30. ESSENTIL QUESTION HEK-IN 9. rlen knows the measures of two angles of a triangle. Eplain how he can find the measure of the third angle. Why does your method work? Houghton Mifflin Harcourt Publishing ompany 432 Unit 5
N Name lass ate 15.2 Independent Practice 6.8. Figure represents a garden crossed by straight walkway. Use the figure for 10 15. 57 Personal Math Trainer P Online ssessment and Intervention 16. n observer at point O sees airplane P directly over airport. The observer measures the angle of the plane at 40.5. 100 32 10. Find m. 88 O Find m P. 40.5 11. Eplain how you found m. The map shows the intersection of three streets in San ntonio s River Walk district. Use the map for 17 18. 12. Find m. ll S Houghton Mifflin Harcourt Publishing ompany 13. Eplain how you found m. 14. Find m. 15. Eplain how you found m. 48 n h y 17. Find the measures of the three angles of the triangle. 18. Eplain how you found the angle measures. Lesson 15.2 433
FOUS ON HIGHER ORER THINKING Work rea 19. Persevere in Problem Solving Find the measure of. Eplain how you found your answer. 83 148 20. ommunicate Mathematical Ideas Eplain how you can use the figure to find the sum of the measures of the angles of quadrilateral. What is the sum? 21. raw onclusions Recall that a right triangle is a triangle with one right angle. One angle of a triangle measures 89.99 degrees. an the triangle be a right triangle? Eplain your reasoning. Houghton Mifflin Harcourt Publishing ompany 434 Unit 5