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Grade 8 - geometry investigation - Rene Rix - model answers

Module by: Pinelands High School. E-mail the author

Summary: model answers for geometry investigation of polygons

Grade 8: Investigation paper on geometry

Section A: Introductory tasks

Task one:

1) 90°90°90^circ

2) 110°110°110^circ

3) 70°70°70^circ

Task two:

  1. 1) J and K are vertices of the regular hexagon
  2. 2) x is an interior angle of the regular hexagon
  3. 3) y is an exterior angle
  4. 4)
    x + y = 180 ° x + y = 180 ° x + y = 180^circ
    (1)

Task three:

1) x=80°x=80°x = 80^circ

2) 90+45=135180−135=45x=45°90+45=135180−135=45x=45°90 + 45 = 135 newline 180 - 135 = 45 newline x = 45^circ

3) 120+30=150180−150=30x=30°120+30=150180−150=30x=30°120 + 30 = 150 newline 180 - 150 = 30 newline x = 30^circ

Section B: Interior angles of a regular polygon

Task one:

  1. 1) 5
  2. 2) 5
  3. 3) 3
  4. 4)
    180 ° 180 ° 180^circ
    (2)
  5. 5)
    3 × 180 = 540 ° 3 × 180 = 540 ° 3 times 180 = 540^circ
    (3)
  6. 6)
    540 ÷ 5 = 108 ° 540 ÷ 5 = 108 ° 540 div 5 = 108^circ
    (4)

Task 2:

Figure 1
Figure 1 (graphics1.png)

Task three:

  1. 1) Number of sides = number of vertices
  2. 2)
    d = v − 3 d = v − 3 d = v - 3
    (5)
  3. 3)
    t = v − 2 t = v − 2 t = v - 2
    (6)
  4. 4)
    s = ( v − 2 ) 180 ° s = ( v − 2 ) 180 ° s = (v - 2)180^circ
    (7)
  5. 5)
    a = ( v − 2 ) 180 ° v a = ( v − 2 ) 180 ° v a = {(v - 2)180^{circ}} over v
    (8)
  6. 6)
    1. a = ( 20 − 2 ) 180 20 = 162 ° a = ( 20 − 2 ) 180 20 = 162 ° a = {(20 - 2)180} over 20 = 162^circ
      (9)
    2. 1800 = ( v − 2 ) 180 = 12 1800 = ( v − 2 ) 180 = 12 1800 = (v - 2)180 = 12
      (10)
    3. 156 = ( v − 2 ) 180 v v / s = 15 156 = ( v − 2 ) 180 v v / s = 15 156 = {(v - 2)180} over v v/s = 15
      (11)

Section C: Exterior angles of a regular polygon

Task one:

  1. 1)
    72 ° 72 ° 72^circ
    (12)
  2. 2) 5
  3. 3)
    360 ° 360 ° 360^circ
    (13)

Task two

Figure 2
Figure 2 (graphics2.png)

Task three:

  1. 1) All 360
  2. 2)
    e = 360 v e = 360 v e = 360 over v
    (14)
  3. 3)
    1. e = 360 16 = 22,5 ° e = 360 16 = 22,5 ° e = 360 over 16 = 22,5^circ
      (15)
    2. 20 = 360 v = 18 20 = 360 v = 18 20 = 360 over v = 18

Section D: Diagonals from each vertex

Task one:

  1. 1) 6
  2. 2) 9
  3. 3)
Figure 3
Figure 3 (graphics3.png)

  1. 1)
    d = v − 3 d = v − 3 d = v - 3
    (16)
  2. 2)
    m = d × v 2 m = d × v 2 m = {d times v} over 2
    (17)
  3. 3)
    m = ( v − 3 ) v 2 m = ( v − 3 ) v 2 m = {(v - 3)v} over 2
    (18)
  4. 4)
    m = ( 15 − 3 ) 15 2 = 90 m = ( 15 − 3 ) 15 2 = 90 m = {(15 - 3)15} over 2 = 90
    (19)
  5. 5)
    170 = ( v − 3 ) v 2 = 20 170 = ( v − 3 ) v 2 = 20 170 = {(v - 3) v} over 2 = 20
    (20)

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