Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Use the diagram below. Is each statement true? Explain.

7. ∠ 1 angle 1  and ∠ 5 angle 5  are adjacent angles.
8. ∠ 3 angle 3  and ∠ 5 angle 5  are vertical angles.
9. ∠ 3 angle 3  and ∠ 4 angle 4  are complementary.
10. ∠ 1 angle 1  and ∠ 2 angle 2  are supplementary.

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

11. supplementary to ∠ AOD angle
12. adjacent and congruent to ∠ AOE angle
13. supplementary to ∠ EOA angle
14. complementary to ∠ EOD angle
15. a pair of vertical angles

See Problem 2.

For Exercises 16–23, can you make each conclusion from the information in the diagram? Explain.

16. ∠ J ≅ ∠ D angle j approximately equal to angle d
17. ∠ JAC ≅ ∠ DAC angle
18. m ∠ JCA = m ∠ DCA m angle
19. m ∠ JCA + m ∠ ACD = 180 m angle
20. A J ¯ ≅ A D ¯ eh j bar , approximately equal to , eh d bar
21. C is the midpoint of J D ¯ . j d bar , .
22. ∠ JAE angle  and ∠ EAF angle  are adjacent and supplementary.

23. ∠ EAF angle  and ∠ JAD angle  are vertical angles.

See Problem 3.

24. Name two pairs of angles that form a linear pair in the diagram below.

    

25. ∠ EFG angle  and ∠ GFH angle  are a linear pair, m ∠ EFG = 2 n + 21 , m angle  and m ∠ GFH = 4 n + 15 . m angle  What are m ∠ EFG m angle  and m ∠ GFH ? m angle

See Problem 4.

26. Algebra In the diagram, G H → g h vector  bisects ∠ FGI . angle

    

    1. Solve for x and find m ∠ FGH . m angle
    2. Find m ∠ HGI . m angle
    3. Find m ∠ FGI . m angle

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