angles

a) 5cm

Length depends on whether you are looking at a print out or on screen

b) 50°

60°

a) 90%

b) 9/24

180 degrees – 45 degrees = 135 degrees

135/360 = 27/72 = 9/24

c) & d) See below

k = 180 -50-95 = 35°

100°

1. At 4:40, hour hand will be 2/3rds of the way between 4 and 5
2. Minute handle at 40
3. So each hour or number on the clock is 30°
4. From 4:40 to 5:00 the degree angle is 10°
5. From 5:00 to 8 (Which is for 40 mins), the angle is 3 x 30 – 90°
6. Add 10 degrees per note 4 and you get 100

Approximately 40°

An acute angle

65°

1. Triangle = 180°
2. 180 – 50 – 130
3. 130/2 = 65

B

1. 180 – 25 – 107 = 48

E

1. Isosceles triangles have 2 angles the same
2. So, if 30 degrees is one of the angles, then this leaves 150 degrees
3. Therefore, 75 degrees is a possible other triangle

285 degrees

1. The internal angle is an actute angle ( Between 0 -90 degrees)
2. Therefore, angle r in this case, is a reflex angle (Greater than 180 degrees less than 360 degrees)
3. The internal angle is around 75 degrees
4. Therefore, r is 360 – 75 = 285 degrees
5. The actual size if measured is 70%. Therefore angle r 290. Any number between 280 and 290 for angle r is acceptable

67°

1. Angle on a straight line is 180°
2. Therefore 180-23-90 = 67

a. 10 seconds

If turn is 360 degrees every 40 seconds, 90 degrees as a right angle would take 1/4 of 40 = 10 seconds

b. 84 turns

In 56 minutes, the sails make 56/1 * 60/40 turns

Again, use of fractions to calculate these types of questions

210º

1. An equilateral triangle is 60º per inside angle. Therefore, the outside to give a right angle is 30
2. In addition , P would be 180 + 3o = 210

a) 8

1. 1. 1. 1. If 64 cars in total, then the following equation will be used to calculate the number of red cars
         2.  ⁶⁴/₁ * ⁴⁵/_360. 
         3. After cross cancellation, this is simplified to:
         4. 64/₁ * ⁵/₄₀
         5. Further cross cancellation:
         6. 8/₁ * ¹/₁

b) 3/8

1. The key here is to remember that the opposite angles when 2 lines cross, create equal angles
2. So given Black and Red are 45º each, this gives 90° in total
3. So remaining in the circle is 360 – 90 = 270
4. Each angle must therefore be 270/2 = 135
5. Every 45 degrees = 1/8th. So 135 = 3/8

a) NE

b) 135º

90 degrees to face North from West . Then a further 45 degrees to get to NE

c) 225º

1. Reflex angle is 360 degrees less the angle from West to NE.
2. 360 less 135 = 225

d) SE

1. 360 degrees in a circle so of the 495, 360 would bring her back to North
2. This leaves 135 degrees. Given 8 markers , each marker is worth 45 degrees
3. 135/45 = 3 so she moves by 3 markers
4. This takes her to SE

a) 18

1. Comedy represents 1/4 of the total pie. This is 25%.
2. The pie is worth 72 students in total
3. So 1/4 x 72 = 18

b) 50º

1. 360 – 90 – 160 – 60 = 50

a) 30º

1. Acute means an angle < 90º. So this is when the hour handle is at 12 and minute handle at 1.
2. 12 numbers on a regular clock so each one is 30º. (360/12)
3. Therefore, at 1 O’Clock, its 30º

b) 15º

1. At 6.30pm, the hour handle is exactly in the middle between 6 & 7. The Minute handle is at exactly 6.
2. A move from 6 to 7 would be 30º
3. So half of this is 15

a) 30º

1. Yellow + Purple is a right angle so is 90º
2. Therefore, Yellow is 30º

b) 25%

1. 100% for the pie chart. Therefore, Red occupies 1/4 of this.
2. 100/1 * 1/4

c) 90

1. 1. ¹⁸⁰/₃₆₀ * ¹⁸⁰/₁
   2. This is 180 degrees/360 degrees * 180. The equation above can be simplified and you should always do this
   3. ¹/₁ * ⁹⁰/₁

a) octagon

b) obtuse

(greater than 90 degrees)

c) i) 3.4cm

c ii) 27.2cm

34mm x 8 = 272mm

Direction you need to turn: Anticlockwise

Angle of turn required: 60 degrees

Like prior word based questions, just break it down 1 sentence at a time:

Start at zero degrees (or think of it as 12 o’clock). 40 degrees clockwise will be to the right

70 degrees anticlockwise will take you a net 30 degrees to the left of zero

90 degrees clockwise turn from there will take you to a net 60 degrees right. So 60 degrees clockwise