Issuu on Google+

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.  angle

Ext.  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 12°. Find (a) the value of n, (b) ∠ 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 ∠ 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.


END OF LESSON The curriculum and its materials were created by City College Math Department. The curriculum design is property of City College. Images are from various sources from the Internet, unless otherwise stated. View lessons from City College Math Department at mathrepublic.wordpress.com Click on the logo for more information on City College.


Angles