Angle Facts
Objectives:
F Grade
D 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’
Recognise corresponding angles and alternate angles

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

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

Vertical
Horizontal 90
90
90
90
360 o
Angles at a Point
1 2
360 o 360 o
3 4
360 o 360 o

Angles at a Point c d b a
Angles at a point add to 360 o
Angle a + b + c + d = 360 0

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

Angles at a Point c d b a
Opposite Angles are equal
Angle a + b = 180 0 because they form a straight line
Angle c + d = 180 0 because they form a straight line
Angle c + b = 180 0 because they form a straight line
Angle d + a = 180 0 because they form a straight line
So a = c and b = d

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

Angle Facts
Now do these:
35 o a
22 o
a = 180 – 35 = 145 o
b = 180 – (22+90) = 68 o b
45 o f
f = 360 – (45+120+110)
f = 360 - 275 = 85 o
110 o
120 o
3g = 360 – (90+60) = 210
g = 70
60 o
116 o c d
Opposite angles are equal
So c = 116 o
d = 180 – 116 = 64 o e
135 o
80 o
e = 360 – (135+80) = 145 o g g g i h
2h
i = 180 - 148 = 32 o
148 o
3h = 180 – i = 148
h = 49.3
.

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.

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.

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 180 o .(Supplementary)

Angles between Parallel Lines

Angles between Parallel Lines

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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