1. Angle Facts
Objectives:
F Grade Express fractions of full turns in degrees
and vice versa
Recognise acute, obtuse, reflex and right angles
Estimate angles and measure them accurately
Use properties of angles at a point and angles
on a straight line
Understand the terms ‘perpendicular lines and
‘parallel lines’
D Grade Recognise corresponding angles and alternate angles

2. Angle Facts
Define: Perpendicular Lines
Two lines at right angles (90o) to each other
Define: Parallel
Straight lines that are always the same distance apart and never meet

3. Angle Facts
Starter:
Name these angles:
Acute
Obtuse
Right Angle
Reflex

4. Angles at a Point 1 2 360o 360o 360o 3 4 360o 360o Vertical Horizontal90
Vertical
Horizontal 1 2
360o
360o
360o 3 4
360o
360o

5. Angles at a point add to 360ob c d
Angles at a point add to 360o
Angle a + b + c + d = 3600

6. Angles at a Point Example: Find angle a. a 75o 85o 360o 80o +90
360o
75o
85o
80o a
Example: Find angle a. 85 75 80 +
240
Angle a = ( )
= = 120o

7. Opposite Angles are equal
Angles at a Point a b c d
Opposite Angles are equal
Angle a + b = 1800 because they form a straight line
Angle c + d = 1800 because they form a straight line
Angle c + b = 1800 because they form a straight line
Angle d + a = 1800 because they form a straight line
So a = c and b = d

8. Angles on a straight line add to 180o
Angles on a Line 90
Angles on a straight line add to 180o
180o
Oblique line
Horizontal line a b
Angles a + b = 180o
70o b x
35o
Angle b = 180 – 70 = 110o
Angle x = 180 – 35 = 145o

9. Angle Facts Now do these: . f = 360 – (45+120+110) f = 360 - 275 = 85ob
22o
116o c d e
135o
80o
148o i
a = 180 – 35 = 145o
b = 180 – (22+90) = 68o
3g = 360 – (90+60) = 210
g = 70
Opposite angles are equal
So c = 116o
d = 180 – 116 = 64o
i = = 32o
3h = 180 – i = 148
e = 360 – (135+80) = 145o
h = 49.3 .

10. Angles between Parallel Lines
Draw a pair of parallel lines with a transversal and measure the 8 angles.
Transversal
Parallel lines remain the same distance apart.
Vertically opposite angles are equal.
Corresponding angles are equal.

11. Angles between Parallel Lines
Draw a pair of parallel lines with a transversal and measure the 8 angles.
Transversal
Parallel lines remain the same distance apart.
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.

12. Angles between Parallel Lines
Draw a pair of parallel lines with a transversal and measure the 8 angles.
Transversal
Parallel lines remain the same distance apart.
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

13. Angles between Parallel Lines

14. Angles between Parallel Lines

15. Angles between Parallel Lines
Name an angle corresponding to the marked angle.
Transversal a d c
Parallel lines remain the same distance apart. e f h g
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

16. Angles between Parallel Lines
Name an angle corresponding to the marked angle.
Transversal a b c
Parallel lines remain the same distance apart. e f h g
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

17. Angles between Parallel Lines
Name an angle corresponding to the marked angle.
Transversal a b d c
Parallel lines remain the same distance apart. f h g
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

18. Angles between Parallel Lines
Name an angle corresponding to the marked angle.
Transversal a b d
Parallel lines remain the same distance apart. e f h g
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

19. Angles between Parallel Lines
Name an angle alternate to the marked angle.
Transversal a b d
Parallel lines remain the same distance apart. e f h g
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

20. Angles between Parallel Lines
Name an angle alternate to the marked angle.
Transversal a b d c
Parallel lines remain the same distance apart. e h g
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

21. Angles between Parallel Lines
Name an angle interior to the marked angle.
Transversal a b c
Parallel lines remain the same distance apart. d e h g
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

22. Angles between Parallel Lines
Name an angle interior to the marked angle.
Transversal a b d c
Parallel lines remain the same distance apart. e h g
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

23. Angles between Parallel Linesd a h e c g f
Name an angle corresponding to the marked angle.
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

24. Angles between Parallel Linesd a e c b g f
Name an angle alternate to the marked angle.
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

25. Angles between Parallel Linesd h e c b g f
Name an angle interior to the marked angle.
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

26. Angles between Parallel Lines
Name in order, the angles that are alternate, interior and corresponding to the marked angle. e h f g d c b
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

27. Angles between Parallel Lines
Name in order, the angles that are alternate, interior and corresponding to the marked angle. d a c h e g f
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

28. Angles between Parallel Lines
Finding unknown angles
 x =
80o
Int. s
 y =
60o
vert.opp. s
 z =
120o
Int. s z
100o
Find the unknown angles stating reasons, from the list below. y x
60o
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

29. Angles between Parallel Lines
Finding unknown angles
 x =
105o
corr. s
 y =
55o
alt. s
 z =
125o
Int. s
105o z
55o
Find the unknown angles stating reasons, from the list below. x y
Vertically opposite angles are equal.
vert.opp. s
Corresponding angles are equal.
corr. s
Alternate angles are equal.
alt. s
Interior angles sum to 180o .(Supplementary)
Int. s

30. Angles between Parallel Lines
Finding unknown angles
 x =
 y =
85o
Int. s
Unknown angles in quadrilaterals and other figures can be found using these properties.
120o
Int. s y
95o
Find the unknown angles stating reasons, from the list below.
60o x
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

31. Angles between Parallel Lines
Finding unknown angles
125o
Int. s
 x =
55o
Int. s
 y =
Unknown angles in quadrilaterals and other figures can be found using these properties.
125o
Int. s
 z = x y
Find the unknown angles stating reasons, from the list below.
55o z
What does this tell you about parallelograms?
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)

32. Angles between Parallel Lines
 c =
 d =
 e =
 f =
 g =
 h =
58o
vert.opp. s
32o
s in tri
58o a b
32o
alt. s
58o
s on line
58o
corr. s e c g f d
52o
s at a point
70o
64o
isos tri h
Mixing it!
64o
isos tri
Vertically opposite angles are equal.
Find the unknown angles stating reasons, from the list below. There may be more than one reason.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
Angle sum of a triangle (180o)
Angle on a line sum to (180o)
Base angles isosceles triangle equal.
Angles at a point sum to 360o

33. Angle Facts Now do these: 65o p 99o 77o 38o 54o 48o 35o z 130o y x w tu s r q v
t = 99o
u = 81o
v = 54o
w = 126o
Corresponding angles
p = 65o
x = 130o
Alternate angles
q = 38o
y = 130o
Corresponding angles
r = 77o
Opposite angles (with r)
or Alternate angles with 77o
s = 77o
z = 35o + 48o = 83o