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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

1) 90°90°90^circ

2) 110°110°110^circ

3) 70°70°70^circ

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)

1) x=80°x=80°x = 80^circ

2) 90+45=135180135=45x=45°90+45=135180135=45x=45°90 + 45 = 135 newline 180 - 135 = 45 newline x = 45^circ

3) 120+30=150180150=30x=30°120+30=150180150=30x=30°120 + 30 = 150 newline 180 - 150 = 30 newline x = 30^circ

### Section B: Interior angles of a regular polygon

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)

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

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

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

1. 1) 6
2. 2) 9
3. 3)

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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