Essay on Business: Harshad Number and B 1

1. (i) 110 2
B1 for 110
(ii) Angles around a point total 360°
B1 for a correct full reason
[2]

2. (a) 132 1 180 − 48
B1 for 132
(b) (i) 66 3 (180 − 48) ÷ 2
B1 for 66
(ii)
3rd angle in triangle = y° (isosceles triangle) y + y + 48 = 180 (angles in triangle sum to 180°)
B1 for isosceles triangle
B1 for either angles in triangle sum to 180° or exterior angle of triangle = sum of two interior opposite angles
[4]

3. 142 4 2x + x + 100 + 47 = 360
2x + x = 360 – 100 – 47 x = 71
Largest angle = 2x =
M1 for 2x + x + 100 + 47 = 360 or 360 – 147 or 213 seen
M1 dep for correctly separating x-terms and non x terms or “360 – 147” ¸ 3
A1 for x = 71provided M2 awarded
A1 ft for 142
[4]

4. (a) 135 3 Exterior angle = = 45
Int angle = 180 - 45
M1 for OR “6” ´ 180 oe
M1 for 180 - “45” OR
A1 cao
(b) 12 2 M1 for
A1 cao
[5]

5. (a) (i) 38 2
B1 for 38
(ii) alternate
B1 for alternate (or Z) angles
(b) 109 2 (180 – 38) ÷ 2 = 142 ÷ 2 = 71
M1 for (180 – “38”) ÷ 2 or 71 seen
A1 ft from (a)(i)
[4]

6. (a) (i) 60 2
B1 cao
(ii) eg top triangle is equilateral
B1 for reason
(b) 150 2
M1 for + 90
A1 ft from (a)(i) if x < 90
SC B1 for “60” + 90 if x < 90
[4]

7. (a) (i) 60 2
B1 for 60
(ii)
B1 for all angles equal so equilateral triangle oe
(b) (i) 130 3
B1 for 130
(ii)
B1 for isosceles triangle oe or 2 angles equal accept ÐQ = ÐR
B1 for angles on a straight line add up to 180°oe (180º could be in working)
(c) 64

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