C Challenge

42. Probability Find the probability that the measure of an interior angle of a regular n-gon is a positive integer when n is an integer and 3 ≤ n ≤ 12 . 3 less than or equal to . n less than or equal to 12 .
43. 1. In the Corollary to the Polygon Angle-Sum Theorem, explain why the measure of an interior angle of a regular n-gon is given by the formulas 180 ( n − 2 ) n fraction 180 open n minus 2 close , over n end fraction and 180 − 360 n . 180 minus , 360 over n , .
    2. Use the second formula to explain what happens to the measures of the interior angles of regular n-gons as n becomes a large number. Explain also what happens to the polygons.
44. ABCDEFGHJK is a regular decagon. A ray bisects ∠ C , angle c comma and another ray bisects ∠ D . angle d . The two rays intersect in the decagon's interior. Find the measure of the acute angles formed by the intersecting rays.

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

45. The car at each vertex of a Ferris wheel holds a maximum of five people. The sum of the interior angle measures of the Ferris wheel is 7740. What is the maximum number of people the Ferris wheel can hold?
46. A rectangle and a square have equal areas. The rectangle has length 9 cm and width 4 cm. What is the perimeter of the square, in centimeters?

47. The Public Garden is located between two parallel streets: Maple Street and Oak Street. The garden faces Maple Street and is bordered by rows of shrubs that intersect Oak Street at point B. What is m ∠ A B C , m angle eh b c comma the angle formed by the shrubs?

    

48. Δ A B C ≅ Δ D E F . cap delta eh b c approximately equal to cap delta d e f . If m ∠ A = 3 x + 4 , m ∠ C = 2 x , m angle , eh equals . 3 x plus 4 , comma m angle , c equals 2 x , comma and m ∠ E = 4 x + 5 , m angle , e equals . 4 x plus 5 , comma what is m ∠ B ? m angle b question mark

Mixed Review

See Lesson 5-7.

49. If A B ¯ ≅ C B ¯ eh b bar , approximately equal to , c b bar and m ∠ A B D < m ∠ C B D , m angle eh b d less than m angle c b d comma which is longer, A D ¯ eh d bar or C D ¯ ? c d bar , question mark Explain.

    

See Lesson 2-5.

Name the property that justifies each statement.

50. 4 ( 2 a − 3 ) = 8 a − 12 4 open 2 eh minus 3 close equals . 8 eh minus 12
51. R S ¯ ≅ R S ¯ r s bar , approximately equal to , r s bar
52. If ∠ 1 ≅ ∠ 4 , angle , 1 approximately equal to , angle 4 comma then ∠ 4 ≅ ∠ 1 . angle , 4 approximately equal to , angle 1 .

Get Ready! To prepare for Lesson 6-2, do Exercises 53 and 54.

See Lessons 4-1 and 4-3.

Use the figure below.

53. Name the postulate or theorem that justifies Δ E F G ≅ Δ G H E . cap delta e f g approximately equal to cap delta g h e .
54. Complete each statement.
    1. ∠ F E G ≅ □ angle f e g approximately equal to white square
    2. ∠ E F G ≅ □ angle e f g approximately equal to white square
    3. ∠ F G E ≅ □ angle f g e approximately equal to white square
    4. E F ¯ ≅ □ e f bar . approximately equal to white square
    5. F G ¯ ≅ □ f g bar . approximately equal to white square
    6. G E ¯ ≅ □ g e bar . approximately equal to white square

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