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
Define: Parallel
Two lines at right angles (90o) to each
other
Straight lines that are always the same
distance apart and never meet
5. a
b
c
d
Angles at a point add to 360o
Angle a + b + c + d = 3600
Angles at a Point
6. 75o
85o
80o
a
Example: Find angle a.
90 90
90 90
360o
Angle a = 360 - (85 + 75 + 80)
= 360 - 240 = 120o
85
75
80
+
240
Angles at a Point
7. 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
Angles at a Point
8. Horizontal line
Oblique line
a
b
Angles a + b = 180o
70o
b
Angle b = 180 – 70 = 110o
x
35o
Angle x = 180 – 35 = 145o
90 90
Angles on a straight line add to 180o
180o
Angles on a Line
9. Angle Facts
Now do these:
f
g
g
g
2h
h
60o
45o 120o
110o
35o
a
b
22o
116o
c
d
e
135o
80o
148o
i
a = 180 – 35 = 145o
b = 180 – (22+90) = 68o
Opposite angles are equal
So c = 116o
d = 180 – 116 = 64o
e = 360 – (135+80) = 145o
f = 360 – (45+120+110)
f = 360 - 275 = 85o
3g = 360 – (90+60) = 210
g = 70
i = 180 - 148 = 32o
3h = 180 – i = 148
h = 49.3
.
10. Parallel lines
remain the same
distance apart.
Transversal
Draw a pair of parallel
lines with a transversal
and measure the 8 angles.
Vertically opposite angles are equal.
Corresponding angles are equal.
Angles between Parallel Lines
11. Parallel lines
remain the same
distance apart.
Transversal
Draw a pair of parallel
lines with a transversal
and measure the 8 angles.
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Angles between Parallel Lines
12. Parallel lines
remain the same
distance apart.
Transversal
Draw a pair of parallel
lines with a transversal
and measure the 8 angles.
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
Angles between Parallel Lines
15. Parallel lines
remain the same
distance apart.
Transversal
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
a
d c
e
g
h
f
Name an angle
corresponding to the
marked angle.
Angles between Parallel Lines
16. Parallel lines
remain the same
distance apart.
Transversal
a b
c
e
g
h
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)
Angles between Parallel Lines
17. Parallel lines
remain the same
distance apart.
Transversal
a b
c
h g
d
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)
Angles between Parallel Lines
18. Parallel lines
remain the same
distance apart.
Transversal
a b
e
h g
d
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)
Angles between Parallel Lines
19. Parallel lines
remain the same
distance apart.
Transversal
a b
e
h g
d
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)
Angles between Parallel Lines
20. Parallel lines
remain the same
distance apart.
Transversal
a b
e
h g
d c
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)
Angles between Parallel Lines
21. Parallel lines
remain the same
distance apart.
Transversal
a b
e
h g
d
c
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)
Angles between Parallel Lines
22. Parallel lines
remain the same
distance apart.
Transversal
a b
e
h g
d c
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)
Angles between Parallel Lines
23. a
f
e
h
g
d
c
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)
Angles between Parallel Lines
24. a
f
e
b g
d
c
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)
Angles between Parallel Lines
25. h
f
e
b g
d
c
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)
Angles between Parallel Lines
26. h
f
e
b
g
d
c
Name in order, the
angles that are
alternate, interior and
corresponding to the
marked angle.
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
Angles between Parallel Lines
27. a
f
e
h
g
d
c
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
Name in order, the
angles that are
alternate, interior and
corresponding to the
marked angle.
Angles between Parallel Lines
28. x
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
Finding unknown angles
100o Find the
unknown
angles stating
reasons, from
the list below.
y
z
60o
x =
y =
z =
80o Int. s
60o vert.opp. s
120o Int. s
Angles between Parallel Lines
29. x
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
Finding unknown angles
105o
Find the
unknown
angles stating
reasons, from
the list below.
y
z
x =
y =
z =
105o corr. s
55o alt. s
125o Int. s
55o
Angles between Parallel Lines
30. x
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
Finding unknown angles
95o Find the
unknown
angles stating
reasons, from
the list below.
y
x =
y =
85o Int. s
120o Int. s
60o
Unknown
angles in
quadrilaterals
and other
figures can be
found using
these
properties.
Angles between Parallel Lines
31. x
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
Finding unknown angles
Find the
unknown
angles stating
reasons, from
the list below.
y
55o
z
x =
y =
z =
What does this tell you about parallelograms?
125o Int. s
125o
55o Int. s
55o
125o Int. s
125o
Unknown
angles in
quadrilaterals
and other
figures can be
found using
these
properties.
Angles between Parallel Lines
32. 70o
a
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
Find the
unknown
angles stating
reasons, from
the list below.
There may be
more than one
reason.
58o vert.opp. s
32o s in tri
58o
32o alt. s
b
d
c
Angle sum of a triangle (180o)
Angle on a line sum to (180o)
58o s on line
e 58o corr. s
52o s at a point
f
g
h
Base angles isosceles triangle equal.
64o isos tri
a =
b =
c =
d =
e =
f =
g =
h = 64o isos tri
Angles at a point sum to 360o
Mixing it!
Angles between Parallel Lines
33. Angle Facts
Now do these:
65o
p
99o
77o
38o
54o
48o
35o
z
130o
y
x
w
t u
s
r
q
v
Corresponding angles
p = 65o
Alternate angles
q = 38o
Corresponding angles
r = 77o
Opposite angles (with r)
or Alternate angles with 77o
s = 77o
t = 99o
v = 54o
u = 81o
w = 126o
x = 130o
y = 130o
z = 35o + 48o = 83o
