52. How many degrees are there in the angle whose complement contains 30° more than the angle itself?

53. Divide an arc of 120° into two arcs, one of which contains 20° more than the other.

54. A circular flower bed is 48 feet in circumference. It is bordered a part of the way with pinks and the rest of the way with mignonette. The edge planted with pinks is 3 times as great as that planted with mignonFind the number of feet of the edge given to

ette. each.

55. John and James started from the same place and ran round a circular race track 120 meters in circumference until they met. John ran 20 meters more than James. How far did each run?

QUERY.

Can you think how the track and the boys running on it would look? It is necessary to form clear pictures in your mind of things described in your problems.

56. John, James, and William ate a round pie 22 inches in circumference. The curved edge of John's piece was 2 inches longer than that of James's and that of James's was 3 inches longer than that of William's. Give the length of curved edge of each piece. What fractional part of the whole pie did each boy eat?

57. The same boys ate another round pie 28 inches in circumference. William's piece was twice as large as James's, and James's was twice as large as John's. Give the length of the curved edge of each piece.

58. Albert, George, and Charles built a fence around a circular lot 300 feet in circumference. Albert built twice as much as George and Charles built 3 times as much as George. How many feet did each build?

59. Mary, Jennie, and Anna embroider the edge of a round tidy 42 inches in circumference. Mary works twice as much as Jennie, and Anna works 3 times as much as Jennie. How many inches of the edge does each embroider?

60. Tom, Fred, and Will whitewashed the fence around a circular lot 60 feet in circumference. Fred whitewashed 3 times as much as Tom, and Will 4 times as much as Tom. How many feet of fence did each whitewash?

61. Mary, Jennie, and Anna decorate a round table 44 inches in circumference. Mary decorates 8 inches more of the edge than Jennie, and Anna twice as many as Mary. How many inches does each decorate?

62. Divide a quadrant into two arcs, one of which is 10° more than the other.

63. Three angles are formed at the same point on the same side of a straight line. The first is 20° greater than the second, and the second is 30° greater than the third. How many degrees has each? Represent the angles.

64. Three angles are formed around a common point. The first contains 15° more than the second, and the second 30° more than the third.

each? Represent.

How many degrees has

65. A long side of a rectangle whose perimeter is 80 centimeters, is 5 centimeters more than 4

times a short side. Find each side.

66. If the angle a is 20° less than twice the angle b, how many degrees are there in each angle?

a/b

E

-F

Um

67. What are parallel lines?

68. Angle a being 107°, how many A degrees are there in each of the other o angles formed by the transversal and three parallels?

69. How many degrees are there in each angle if angle c is 50° more than angle e?

70. How many degrees are there in each angle if angle c is 30° less than 3 times angle e?

e

CHAPTER V.

RECTANGLES.

NOTE. A Polygon is a plane figure bounded by straight lines. When a polygon is bounded by four straight lines it is called a Quadrilateral. When the opposite sides of a quadrilateral are parallel it is called a Parallelogram. When a parallelogram has four right angles it is called a Rectangle. When the sides of a rectangle are all equal it is called a Square. A parallelogram which is not a rectangle is called a Rhomboid.

1. Draw a polygon. Is a sector a polygon?

2. Draw a quadrilateral.

3. Draw a parallelogram.

4. Draw a rectangle.

5. Draw a square and show that it is entitled to six different names.

6. Draw a rhomboid and show to how many names it is entitled.

7. To how many names is a rectangle entitled?

8. To how many names is a triangle entitled?

9. Construct a rectangle having 3 rows of 1-inch squares, each row containing 8 squares.

square inches does it cover?

How many

NOTE. The amount of surface which a figure covers is called its Area.

10. What is the area of a rectangle consisting of 2 rows of 1-inch squares, each row containing 4 squares?

11. What is the area of a rectangle consisting of 3 rows of 1-inch squares, 7 squares in a row? How long is its perimeter?

12. Draw a rectangle whose base is 5 inches and altitude 4 inches. How many square inches in area is it?

NOTE. - The lower base of a rectangle is either one of the sides upon which it may be supposed to stand, the upper base is the side opposite the lower base, and the altitude is the distance between the bases, measured perpendicularly.

13. In the rectangle ABCD, what line is the lower base? The upper base? What lines represent the altitude? If we turn the rectangle and consider AC the lower base, what lines represent the altitude?

14. Show the truth of the principle:

B

D

PRINCIPLE 16. The area of a rectangle is equal to

the product of its base and altitude.

15. What is the area of a rectangle whose base is 12 inches and altitude half as much?

16. Find the area of a rectangle whose base is 5 centimeters and altitude 8 centimeters.

17. Base = 71⁄2 inches; altitude = 5 inches; required the area of rectangle.

18. Base = 163 inches; altitude of base; required the area of rectangle.

19. Base twice the altitude; sum of base and altitude 15 inches; find the area of rectangle.

SUGGESTION.- Let x = altitude.