**a) 5cm**

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

**b) 50°**

**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°**

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

**Approximately 40°**

An acute angle

**65°**

- Triangle = 180°
- 180 – 50 – 130
- 130/2 = 65

**B**

- 180 – 25 – 107 = 48

**E**

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

**285 degrees**

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

**67°**

- Angle on a straight line is 180°
- 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**

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

**a) 8**

- If 64 cars in total, then the following equation will be used to calculate the number of red cars
^{ 64}/_{1}*^{45}/_{360. }- After cross cancellation, this is simplified to:
- 64/
_{1}*^{5}/_{40} - Further cross cancellation:
- 8/
_{1}*^{1}/_{1}

**b) 3/8**

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

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

**d) SE**

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

**a) 18**

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

**b) 50º**

- 360 – 90 – 160 – 60 = 50

**a) 30º**

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

**b) 15º**

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

**a) 30º**

- Yellow + Purple is a right angle so is 90º
- Therefore, Yellow is 30º

**b) 25%**

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

**c) 90**

^{180}/_{360}*^{180}/_{1}- This is 180 degrees/360 degrees * 180. The equation above can be simplified and you should always do this
^{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