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1、15 Polygons MEP Y8 Practice Book B15.1Angle FactsIn this section we revise some basic work with angles, and begin by using the three rules listed below:The angles at a point add up to 360 , e.g.baca + b + c = 360 The angles on a straight line add up to 180 , e.g.efe + f= 180 The angles in a triangle
2、 add up to 180 , e.g.xwyw + x + y = 180 Example 1Determine the size of angle a in the diagram shown.81 92Solutiona 10081 + 92 + 100 + a=360 (angle sum at a point)a + 273 =360a=87 Example 2Determine the size of angle d in the diagram shown.105Solutiond42105 + 42 + d=180(angle sum in a triangle)147 +
3、d=180d = 33 52MEP Y8 Practice Book BExample 3Determine the size of angle n in the diagram shown.27Solutionnn + 27 = 180 (angle sum on a line)n = 153 Exercises1. Calculate the sizes of the angles marked by letters in the following diagrams:(a)(b)71123 110b89a37(c)(d)931911333c 1078777d2. Calculate th
4、e sizes of the unknown angles in the following triangles:(a)(b)335111168(c)(d)9239435315.1MEP Y8 Practice Book B3. Calculate the sizes of the angles marked by the letter x in the following diagrams:(a)(b)32x49x81(c)(d)431719xx947231404. The diagram shows an isosceles triangle.What are the sizes of t
5、he two angles marked a and b ?abb5. Calculate the sizes of the angles marked a and b in the diagram.143a736. The diagram opposite shows two intersectingstraight lines. Calculate the sizes of thea47bcangles marked a, b and c in the diagram.What do you notice aboutangles a and c ?c7. The diagram oppos
6、ite shows a rectangleand its diagonals. Calculate the sizes ofbthe angles marked a, b and c.a373754MEP Y8 Practice Book B8. Determine the sizes of the angles marked a, b and c in the diagram shown.72ab1923cc9. PQR is a straight line. Determine the sizes of the angles marked a, b and c in the triangl
7、es shown.P10. Calculate the sizes of the angles marked a, b, c, d and e in the triangles shown.3961a 91 b85QRb37cad 12313e55MEP Y8 Practice Book B15.2Angle Properties of PolygonsIn this section we calculate the size of the interior and exterior angles for different regular polygons.The following dia
8、gram shows a regular hexagon:The angles markedinterior angles ofthe hexagon.are theThe angles marked arethe exterior angles of thehexagon.In a regular polygon the sides are all the same length and the interior angles are all the same size.Note that, for any polygon:interior angle + exterior angle =
9、180 .Since the interior angles of a regular polygon are all the same size, it follows that the exterior angles are also equal to one another.One complete turn of the hexagon above will rotate any one exterior angle to each of the others in turn, which illustrates the following result:The exterior an
10、gles of any polygon add up to360 .Example 1Calculate the sizes of the interior and the exterior angles of a regular hexagon.Hence determine the sum of the interior angles.SolutionThe exterior angles of a regular hexagon are all equal, as shown in the previous diagram.56MEP Y8 Practice Book BTherefor
11、e the exterior angle of a regular hexagon=360 6=60 So the interior angle of a regular hexagon=180 - 60 =120 The sum of the interior angles=6 120 = 720 Example 2The exterior angle of a regular polygon is40 .Calculate:(a) the size of the interior angle,(b) the number of sides of the polygon.Solution(a) Interior angle + exterior angle = 180 Interior angle= 180 - 40 = 140 (b) The number of sides can be determined by dividing 360 by the size of the exterior angles, giving360=940so the polygon has 9 sides.In a regular polygon:exterior angle=360 the number of sidesnumber of sides=360
