ANGLES

Properties

2

If PQ is straight line, then ___________ (_____________)

___________ (_____________)

If AB & BC are straight lines, then ______ & ______(_________)

3

Solve

4

Solve

5

Parallel Lines

Properties

6

If AB and CD are parallel lines. a) ∠s = ∠r (_________________) b) ∠q = ∠s (_________________) c) ∠p + ∠q = 180° (_________________)

7

Solve

8

Solve

9

Solve

10

Solve

(i) (ii) (iii)

Angle BAX, Angle CBX, Angle BDX.

11

Solve

12

Bearings

13

How to Read Bearings

To read the bearing of B from A: 1. Draw the North line from A. 2. Join A to B. 3. From A, measure the clockwise angle. 4. Bearing is always written in 3 digit.

14

Solve

Useful properties - Sum of interior angles

Find the bearing of (a)#A from O, (b)#B from A, (c) A from B.

15

Solve

Useful properties - Alternate angles

Find the bearing of (d) O from B.

16

Solve

Q1. The points P, Q and R form an equilateral triangle and the bearing of Q from P is. Find (a) the bearing of R from P, (b) the bearing of R from Q, (c) the bearing of P from R.

17

Solve Q2. In the diagram, R is due east of P and angle PQR = 800. If the bearing of Q from R is 2000, find (a) angle QRP, (b) the bearing of Q from P.

18

Angles of Polygon

Properties

19

∠p + ∠q + ∠r = _____ (∠ sum of a ∆)

∠a + ∠b + ∠c + ∠d = _____

Properties

20

Sum of int. angles = (n – 2) × 180o

Properties

21

If the polygon is regular, Size of an angle = _________

Properties

22

Int. Â angle

Ext. Â angle

Int. angle + Ext. angle = ________

23

Properties

Sum of exterior angles = ___________________

24

Summary

1. Sum of interior angles = ___________________

2. Sum of exterior angles = ___________________

3. 1 Interior + 1 Exterior = ___________________

25

Solve

25

Solve Q1. Find the unknown value.

26

Solve

26

Solve Q2. Find the unknown value.

27

Solve

Q3. Given that a regular n-sided polygon has an interior angle twice the exterior angle, find the number of sides that the polygon has.

28

Solve

Q4. The size of each interior angle of a regular polygonis 11 times the size of each exterior angle. (a) Find the size of each exterior angle. (b) How many sides does the polygon have?

29

Solve

Q5. An exterior angle of an octagon is 66째 while the other seven exterior angles are each equal to x째. a) Calculate the value of x. b) Find the smallest interior angle of the octagon.

30

Solve Q6. AB, BC and CD are three adjacent sides of a regular 12-sided polygon. Calculate the values of (a) ∠ ABC, (b) ∠ACD.

31

Solve

Q7. The diagram shows part of a regular polygon with n sides. Each exterior angle of this polygon is 12Â°. Find (a) the value of n, (b) âˆ ACD.

B

A

C D E

32

Angles on Circles

33

Terminology

OR: ___________ PQ: ___________

34

Terminology

∠FXM = 90° (_________________________)

35

Terminology

AC: _____________ ABC: ______________ Shaded part: _____________

36

Properties

∠FYM = ∠FXM (_________________________________)

Properties

37

∠ADC + ∠ABC = 180° ∠BAD + ∠BCD = 180° (______________________________)

Properties

38

∠FOM = 2 × ∠FXM (__________________________________)

Properties

39

∠OTX = 90° (______________________)

40

Solve

Q1. What is the value of x? State the reason.

41

Solve

Q2. What is the value of x? State the reason.

42

Solve

Q3. What is the value of x? State the reason.

43

Solve

Q4. What is the value of x? State the reason.

44

Solve

Q5. What is the value of x? State the reason.

45

Solve

Q6. What is the value of x? State the reason.

46

Solve

Q7. What is the value of x? State the reason.

47

Solve

Q8. What is the value of x? State the reason.

48

Solve

Q9. What is the value of x? State the reason.

49

Solve

Q10. What is the value of x? State the reason.

50

Solve

Q11. What is the value of x? State the reason.

51

Solve

Q12. What is the value of x? State the reason.

52

Solve

Q13. What is the value of x? State the reason.

53

Solve Q14. Find ∠ OKN

Find ∠ BAC

54

Solve Q15. Find âˆ ACB

Find unknown

55

Solve

Q16. Find ∠ APD

56

Solve # Q17. In the figure, QS is a diameter and T is the intersection of QS and PR. # If ∠ RSQ = 72° and ∠ SQP = 28°, find # (a)#∠ SPR,# (b) ∠ PTS.

57

Solve Q18. O is the centre of a circle. PCQ is tangent to the circle at C. ∠ ABC = 98° and ∠ BCP = 55°. Stating your reasons clearly, find (a) reflex ∠ AOC ,# (b)# ∠ BAO.

58

Solve Q19. AC is the diameter of the circle. XAB and XDC are straight lines and DE =EC. Given that ∠ BXC = 20º and ∠ ACB = 50º, find, giving your reasons in the working space, (a) ∠ BDC, (b) ∠ XCA, (c) ∠ DEC.

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