See Problem 2.

Point O is the center of regular hexagon HEXAGN. Find the image of the given point or segment for the given rotation.

17. 60 ° 60 degrees  rotation of E about O
18. 120 ° 120 degrees  rotation of A X ¯ eh x bar  about O
19. 240 ° 240 degrees  rotation of N G ¯ n g bar  about O
20. 360 ° 360 degrees  rotation of H about O

See Problem 3.

Native American Art Find the angle of rotation about C that (a) maps Q to X and (b) maps X to Q.

See Problem 4.

For Exercises 24–29, copy Δ X Y Z . cap delta x y z .  Draw the image of Δ X Y Z cap delta x y z  for the given composition of rotations about the given point.

24. 45 ° , 45 degrees comma  then 45 ° ; 45 degrees semicolon  X
25. 45 ° , 45 degrees comma  then 45 ° ; 45 degrees semicolon  Y
26. 30 ° , 30 degrees comma  then 30 ° ; 30 degrees semicolon  Z
27. 20 ° , 20 degrees comma  then 160 ° ; 160 degrees semicolon  Z
28. 135 ° , 135 degrees comma  then 135 ° ; 135 degrees semicolon  Y
29. 180 ° , 180 degrees comma  then 180 ° ; 180 degrees semicolon  X

B Apply

30. In the diagram below, M ′ N ′ ¯ m prime , n prime bar  is the rotation image of M N ¯ m n bar  about point E. Name all pairs of congruent angles and all pairs of congruent segments in the diagram.

    

31. Language Arts The symbol is called a schwa. It is used in dictionaries to represent neutral vowel sounds such as a in ago, i in sanity, and u in focus. What transformation maps a to a lowercase e?

Find the angle of rotation about C that maps the black figure to the blue figure.

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