THINK AND DISCUSS 1. Explain why any two right angles are supplementary. 2. Is it possible for a pair of vertical angles to also be adjacent? Explain. 3. GET ORGANIZED Copy and complete the graphic organizer below. In each box, draw a diagram and write a definition of the given angle pair. `>ViÌÊ>}iÃ
*>ÀÃÊv }iÃ
i>ÀÊ«>À 6iÀÌV>Ê>}iÃ
1-4
«iiÌ>ÀÞ >}ià -Õ««iiÌ>ÀÞ >}iÃ
Exercises
KEYWORD: MG7 1-4 KEYWORD: MG7 Parent
GUIDED PRACTICE Vocabulary Apply the vocabulary from this lesson to answer each question. 1. An angle measures x°. What is the measure of its complement? What is the measure of its supplement? 2. ∠ABC and ∠CBD are adjacent angles. Which side do the angles have in common? SEE EXAMPLE
1
p. 28
Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. 3. ∠1 and ∠2 5. ∠2 and ∠4
SEE EXAMPLE
2
p. 29
SEE EXAMPLE
3
p. 29
SEE EXAMPLE 4 p. 30
SEE EXAMPLE
5
4. ∠1 and ∠3
Ó
Î
{
6. ∠2 and ∠3
£
Find the measure of each of the following. 7. supplement of ∠A
8. complement of ∠A
9. supplement of ∠B
10. complement of ∠B
ÈÝÊÊx®Â n£°ÓÂ
11. Multi-Step An angle’s measure is 6 degrees more than 3 times the measure of its complement. Find the measure of the angle. 12. Landscaping A sprinkler swings back and forth between A and B in such a way that ∠1 ∠2. ∠1 and ∠3 are complementary, and ∠2 and ∠4 are complementary. If m∠1 = 47.5°, find m∠2, m∠3, and m∠4.
13. Name each pair of vertical angles.
Î
{
£
Ó
p. 30
1- 4 Pairs of Angles
31
PRACTICE AND PROBLEM SOLVING Independent Practice For See Exercises Example
14–17 18–21 22 23 24
1 2 3 4 5
Extra Practice Skills Practice p. S4 Application Practice p. S28
Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. 14. ∠1 and ∠4
15. ∠2 and ∠3
16. ∠3 and ∠4
17. ∠3 and ∠1
Ó Î
£ {
Given m∠A = 56.4° and m∠B = (2x - 4)°, find the measure of each of the following. 18. supplement of ∠A
19. complement of ∠A
20. supplement of ∠B
21. complement of ∠B
22. Multi-Step An angle’s measure is 3 times the measure of its complement. Find the measure of the angle and the measure of its complement. 23. Art In the stained glass pattern, ∠1 ∠2. ∠1 and ∠3 are complementary, and ∠2 and ∠4 are complementary. If m∠1 = 22.3°, find m∠2, m∠3, and m∠4.
24. Name the pairs of vertical angles.
1
*
3 1
4 2
+
/ -
, 6
25. Probability The angle measures 30°, 60°, 120°, and 150° are written on slips of paper. You choose two slips of paper at random. What is the probability that the angle measures are supplementary? Multi-Step ∠ABD and ∠BDE are supplementary. Find the measures of both angles. 26. m∠ABD = 5x°, m∠BDE = (17x - 18)° 27. m∠ABD = (3x + 12)°, m∠BDE = (7x - 32)° 28. m∠ABD = (12x - 12)°, m∠BDE = (3x + 48)° Multi-Step ∠ABD and ∠BDC are complementary. Find the measures of both angles. 29. m∠ABD = (5y + 1)°, m∠BDC = (3y - 7)° 30. m∠ABD = (4y + 5)°, m∠BDC = (4y + 8)° 31. m∠ABD = (y - 30)°, m∠BDC = 2y° 32. Critical Thinking Explain why an angle that is supplementary to an acute angle must be an obtuse angle.
33. This problem will prepare you for the Multi-Step Test Prep on page 34. H is in the interior of ∠JAK. m∠JAH = (3x - 8)°, and m∠KAH = (x + 2)°. Draw a picture of each relationship. Then find the measure of each angle. a. ∠JAH and ∠KAH are complementary angles. b. ∠JAH and ∠KAH form a linear pair. c. ∠JAH and ∠KAH are congruent angles.
32
Chapter 1 Foundations for Geometry
Determine whether each statement is true or false. If false, explain why. 34. If an angle is acute, then its complement must be greater than its supplement. 35. A pair of vertical angles may also form a linear pair. 36. If two angles are supplementary and congruent, the measure of each angle is 90°. 37. If a ray divides an angle into two complementary angles, then the original angle is a right angle. 38. Write About It Describe a situation in which two angles are both congruent and complementary. Explain.
39. What is the value of x in the diagram? 15 45 30
ÝÂ
90
ÝÂ
40. The ratio of the measures of two complementary angles is 1 : 2. What is the measure of the larger angle? (Hint: Let x and 2x represent the angle measures.) 30° 45° 60° 120° 41. m∠A = 3y, and m∠B = 2m∠A. Which value of y makes ∠A supplementary to ∠B? 10 18 20 36 42. The measures of two supplementary angles are in the ratio 7 : 5. Which value is the measure of the smaller angle? (Hint: Let 7x and 5x represent the angle measures.) 37.5 52.5 75 105
CHALLENGE AND EXTEND 43. How many pairs of vertical angles are in the diagram? 44. The supplement of an angle is 4 more than twice its complement. Find the measure of the angle. 45. An angle’s measure is twice the measure of its complement. The larger angle is how many degrees greater than the smaller angle? 46. The supplement of an angle is 36° less than twice the supplement of the complement of the angle. Find the measure of the supplement.
SPIRAL REVIEW Solve each equation. Check your answer. (Previous course) 47. 4x + 10 = 42
48. 5m - 9 = m + 4
49. 2(y + 3) = 12
50. -(d + 4) = 18
Y is between X and Z, XY = 3x + 1, YZ = 2x - 2, and XZ = 84. Find each of the following. (Lesson 1-2) 51. x
52. XY
53. YZ
XY bisects ∠WYZ. Given m∠WYX = 26°, find each of the following. (Lesson 1-3) 54. m∠XYZ
55. m∠WYZ
1- 4 Pairs of Angles
33
