Angle Facts

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
3
Angle Facts
Starter
Name these angles
Acute
Obtuse
Right Angle
Reflex
4
Angles at a Point
360o
360o
360o
360o
360o
5
Angles at a Point
6
Angles at a Point
Angle a 360 - (85 75 80) 360
- 240 120o
7
Angles at a Point
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 Line
Oblique line
Angle x 180 35 145o
Angle b 180 70 110o
9
Angle Facts
f 360 (45120110)
f 360 - 275 85o
a 180 35 145o
b 180 (2290) 68o
3g 360 (9060) 210
g 70
Opposite angles are equal So c 116o d
180 116 64o
i 180 - 148 32o
3h 180 i 148
e 360 (13580) 145o
10
Angles between Parallel Lines
Draw a pair of parallel lines with a transversal
and measure the 8 angles.
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.
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.
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.
a
d
c
Parallel lines remain the same distance apart.
e
f
g
h
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.
a
b
c
Parallel lines remain the same distance apart.
e
f
g
h
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.
a
b
c
d
Parallel lines remain the same distance apart.
f
g
h
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.
a
b
d
Parallel lines remain the same distance apart.
e
f
g
h
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.
a
b
d
Parallel lines remain the same distance apart.
e
f
g
h
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.
a
b
d
c
Parallel lines remain the same distance apart.
e
g
h
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.
a
b
c
Parallel lines remain the same distance apart.
d
e
g
h
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.
a
b
d
c
Parallel lines remain the same distance apart.
e
g
h
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
23
Angles between Parallel Lines
d
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 Lines
d
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 Lines
d
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
b
c
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
? y
? z
Find the unknown angles stating reasons, from the
list below.
100o
z
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
? y
? z
105o
Find the unknown angles stating reasons, from the
list below.
55o
z
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
Unknown angles in quadrilaterals and other
figures can be found using these properties.
Find the unknown angles stating reasons, from the
list below.
95o
y
x
60o
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
31
Angles between Parallel Lines
? x
Finding unknown angles
? y
Unknown angles in quadrilaterals and other
figures can be found using these properties.
? z
y
x
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
58o
b
a
c
e
f
g
d
70o
Mixing it!
h
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
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