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 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.