Use the Diagram at the Right. Is Each Statement True? Explain

Name

Class

Date

Exploring Angle Pairs

1-5

Practice

Use the diagram at the right. Is each statement true? Explain.

1. Ð2 and Ð5 are adjacent angles.

2. Ð1 and Ð4 are vertical angles.

3. Ð4 and Ð5 are complementary.

Name an angle or angles in the diagram described by each of the following.

4. complementary to ÐBOC

5. supplementary to ÐDOB

6. adjacent and supplementary to ÐAOC

Use the diagram below for Exercises 7 and 8. Solve for x.
Find the angle measures.

7. mÐAOB = 4x - 1; mÐBOC = 2x + 15; mÐAOC = 8x + 8

8. mÐCOD = 8x + 13; mÐBOC = 3x - 10; mÐBOD = 12x - 6

9. ÐABC and ÐEBF are a pair of vertical angles; mÐABC = 3x + 8 and
mÐEBF = 2x + 48. What are mÐABC and mÐEBF?

10. ÐJKL and ÐMNP are complementary; mÐJKL = 2x - 3 and mÐMNP = 5x + 2. What are mÐJKL and mÐMNP?

For Exercises 11–14, can you make each conclusion from the information in the diagram? Explain.

11. Ð3 @ Ð4 12. Ð2 @ Ð4

13. mÐ1 + mÐ5 = mÐ3 14. mÐ3 = 90

15. bisects ÐJKL. If mÐJKM = 86, what is mÐJKL?

16. bisects ÐRST. If mÐRST = 62, what is mÐRSV?

Prentice Hall Gold Geometry • Teaching Resources

Name

Class

Date

Exploring Angle Pairs

1-5

Practice (continued)

Form G

bisects ÐPQR. Solve for x and find mÐPQR.

17. mÐPQS = 3x; mÐSQR = 5x - 20

18. mÐPQS = 2x + 1; mÐRQS = 4x - 15

19. mÐPQR = 3x - 12; mÐPQS = 30

20. mÐPQS = 2x + 10; mÐSQR = 5x - 17

For Exercises 21–24, can you make each conclusion from the information in the diagram below? Explain.

21. ÐDAB and ÐCDB are congruent.

22. ÐADB and ÐCDB are complementary.

23. ÐADB and ÐCDB are congruent.

24. ÐADB and ÐBCD are congruent.

25. Algebra ÐMLN and ÐJLK are complementary, mÐMLN = 7x - 1, and
mÐJLK = 4x + 3.

a. Solve for x.

b. Find mÐMLN and mÐJKL.

c. Show how you can check your answer.

26. Reasoning Describe all the situations in which the following statements are true.

a. Two vertical angles are also complementary.

b. A linear pair is also supplementary.

c. Two supplementary angles are also a linear pair.

d. Two vertical angles are also a linear pair.

27. Open-Ended Write and solve an equation using an angle bisector to find the measure of an angle.

Prentice Hall Gold Geometry • Teaching Resources