Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Concept explainers

Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
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Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
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Can you help me with 1-19 please 

CONCEPT SUMMARY For Your Notebook Interpreting a Diagram There are some things you can conclude from a diagram, and some you cannot. For example, here are some things that you can conclude from the diagram at the right: B • All points shown are coplanar. • Points A, B, and Care collinear, and B is between A and C. • AC, BD, and BẺ intersect at point B. • ZDBE and ZEBC are adjacent angles, and ZABC is a straight angle. • Point E lies in the interior of Z DBC. In the diagram above, you cannot conclude that AB = BC, that ZDBE = ZEBC, or that ZABD is a right angle. This information must be indicated, as shown at the right. DO HOMEWORK 1.5 EXERCISES = See WORKED-OUT SOLUTIONS KEY Exs. 9, 21, and 47 * = STANDARDIZED TEST PRACTICE Exs. 2, 16, 30, and 53 = MULTIPLE REPRESENTATIONS Ex. 55 SKILL PRACTICE 1. VOCABULARY Sketch an example of adjacent angles that are complementary. Are all complementary angles adjacent angles? Explain. 2. * WRITING Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain. EXAMPLE 1 IDENTIFYING ANGLES Tell whether the indicated angles are adjacent. for Exs. 3-7 3. ZABD and Z DBC 4. ZWXYand 2XYZ 5. ZLQM and Z NQM M В IDENTIFYING ANGLES Name a pair of complementary angles and a pair of supplementary angles. 6. 7. 150 T\60° S 38 Chapter 1 Essentials of Geometry
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Transcribed Image Text:CONCEPT SUMMARY For Your Notebook Interpreting a Diagram There are some things you can conclude from a diagram, and some you cannot. For example, here are some things that you can conclude from the diagram at the right: B • All points shown are coplanar. • Points A, B, and Care collinear, and B is between A and C. • AC, BD, and BẺ intersect at point B. • ZDBE and ZEBC are adjacent angles, and ZABC is a straight angle. • Point E lies in the interior of Z DBC. In the diagram above, you cannot conclude that AB = BC, that ZDBE = ZEBC, or that ZABD is a right angle. This information must be indicated, as shown at the right. DO HOMEWORK 1.5 EXERCISES = See WORKED-OUT SOLUTIONS KEY Exs. 9, 21, and 47 * = STANDARDIZED TEST PRACTICE Exs. 2, 16, 30, and 53 = MULTIPLE REPRESENTATIONS Ex. 55 SKILL PRACTICE 1. VOCABULARY Sketch an example of adjacent angles that are complementary. Are all complementary angles adjacent angles? Explain. 2. * WRITING Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain. EXAMPLE 1 IDENTIFYING ANGLES Tell whether the indicated angles are adjacent. for Exs. 3-7 3. ZABD and Z DBC 4. ZWXYand 2XYZ 5. ZLQM and Z NQM M В IDENTIFYING ANGLES Name a pair of complementary angles and a pair of supplementary angles. 6. 7. 150 T\60° S 38 Chapter 1 Essentials of Geometry
EXAMPLE 2 for Exs. 8-16 COMPLEMENTARY ANGLES 21 and 22 are complementary angles. Given the measure of Z1, find m/2. 8. m21 = 43° 9 mz1 = 21° 10. mz1 = 89° 11. m21 = 5° SUPPLEMENTARY ANGLES 21 and 2 are supplementary angles. Given the measure of Z1, find m2. 12. m21 = 60° 13. т21-D 155° 14. m21 = 130° 15. m21 = 27° 16. * MULTIPLE CHOICE The arm of a crossing gate moves 37° from vertical. How many more degrees does the arm have to move so that it is horizontal? A 37° B 53° 37 © 90° 143 EXAMPLE 3 O ALGEBRA Find m/DEG and m2 GEF. for Exs. 17-19 17. 18. 19. De G. G' (18x – 9) (4x + 13) (7x – 3) (12x – 7)°. 6x 4x° E E EXAMPLE 4 for Exs. 20-27 IDENTIFYING ANGLE PAIRS Use the diagram below. Tell whether the angles are vertical angles, a linear pair, or neither. 21) 21 and 2 20. 21 and 24 22. 23 and 25 23. 22 and 23 24. 27, 28, and 25. 25 and 26 26. 26 and 27 27. 25 and 29 EXAMPLE 5 28. O ALGEBRA Two angles form a linear pair. The measure of one angle is 4 times the measure of the other angle. Find the measure of each angle. for Exs. 28-30 29. ERROR ANALYSIS Describe and correct the error made in finding the value of x. x° + 3x° = 180° 4x = 180 3x x = 45 30. * MULTIPLE CHOICE The measure of one angle is 24° greater than the measure of its complement. What are the measures of the angles? A 24° and 66° ® 24° and 156° © 33" and 57° O 78° and 102° ALGEBRA Find the values of x and y. 31. 32. 33. (9x + 20)° (8x+ 26)° 2y (4x – 100)° (3y + 30)(x + 5)° 2y 7x (5y + 38)° 3x 1.5 Describe Angle Pair Relationships 39 ....... .....
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Transcribed Image Text:EXAMPLE 2 for Exs. 8-16 COMPLEMENTARY ANGLES 21 and 22 are complementary angles. Given the measure of Z1, find m/2. 8. m21 = 43° 9 mz1 = 21° 10. mz1 = 89° 11. m21 = 5° SUPPLEMENTARY ANGLES 21 and 2 are supplementary angles. Given the measure of Z1, find m2. 12. m21 = 60° 13. т21-D 155° 14. m21 = 130° 15. m21 = 27° 16. * MULTIPLE CHOICE The arm of a crossing gate moves 37° from vertical. How many more degrees does the arm have to move so that it is horizontal? A 37° B 53° 37 © 90° 143 EXAMPLE 3 O ALGEBRA Find m/DEG and m2 GEF. for Exs. 17-19 17. 18. 19. De G. G' (18x – 9) (4x + 13) (7x – 3) (12x – 7)°. 6x 4x° E E EXAMPLE 4 for Exs. 20-27 IDENTIFYING ANGLE PAIRS Use the diagram below. Tell whether the angles are vertical angles, a linear pair, or neither. 21) 21 and 2 20. 21 and 24 22. 23 and 25 23. 22 and 23 24. 27, 28, and 25. 25 and 26 26. 26 and 27 27. 25 and 29 EXAMPLE 5 28. O ALGEBRA Two angles form a linear pair. The measure of one angle is 4 times the measure of the other angle. Find the measure of each angle. for Exs. 28-30 29. ERROR ANALYSIS Describe and correct the error made in finding the value of x. x° + 3x° = 180° 4x = 180 3x x = 45 30. * MULTIPLE CHOICE The measure of one angle is 24° greater than the measure of its complement. What are the measures of the angles? A 24° and 66° ® 24° and 156° © 33" and 57° O 78° and 102° ALGEBRA Find the values of x and y. 31. 32. 33. (9x + 20)° (8x+ 26)° 2y (4x – 100)° (3y + 30)(x + 5)° 2y 7x (5y + 38)° 3x 1.5 Describe Angle Pair Relationships 39 ....... .....
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