1. ANGLES ON A STRAIGHT LINE ADD UP TO 180°
25/02/2019
ANGLES ON A STRAIGHT LINE ADD UP TO 180°

2. Angles on a straight line add up to 180
25/02/2019
Angles on a straight line add up to 180 a b
a + b = 180°
because there are 180° in a half turn.

3. 25/02/2019 Examples x b 70o 35o Angle x = 180 – 35 = 145o
Angle b = 180 – 70 = 110o
Angle x = 180 – 35 = 145o

4. Task Find the size of the missing angles
25/02/2019
Task Find the size of the missing angles x
47o 1
114o y 2 3 4
76o a
82o b
Angle x = 180 – 47 = 133o
Angle y = 180 – 114 = 66o
Angle a = 180 – 76 = 104o
Angle b = 180 – 82 = 98o

5. 25/02/2019
43°
65°
44°
122°
60°
93°
90°
110°
30°
66°

6. VERTICALLY OPPOSITE ANGLES ARE EQUAL
25/02/2019
VERTICALLY OPPOSITE ANGLES ARE EQUAL

7. 25/02/2019
When two lines intersect, two pairs of vertically opposite angles are formed. a d b c
a = c
and
b = d
Vertically opposite angles are equal

8. 25/02/2019 b 35 a
Find the size of the angles a and b giving a reason

9. ANGLES AT A POINT ADD UP TO 360°
25/02/2019
ANGLES AT A POINT ADD UP TO 360°

10. Angles around a point add up to 360
25/02/2019
Angles around a point add up to 360 b a c d
a + b + c + d = 360
because there are 360 in a full turn.

11. 25/02/2019 Example a 75o 85o 80o + Angle a = 360 - (85 + 75 + 80)
240
Angle a = ( )
= = 120o

12. 25/02/2019
Examples
You might also need to use other angle rules and knowledge to help you solve problems involving angles at a point
167° a
69°
68° d
103°
43° c
43° b
137°

13. ANGLES IN A TRIANGLE ADD UP TO 180°
25/02/2019
ANGLES IN A TRIANGLE ADD UP TO 180°

14. The angles in a triangle add up to 180°
25/02/2019 a b c
For any triangle,
a + b + c = 180°
The angles in a triangle add up to 180°

15. 25/02/2019 Examples 65o Calculate angle a a 27o Calculate angle a a

16. Calculate angles a, b and c
25/02/2019
Examples
Calculate angles a, b and c a b c
Since the triangle is equilateral,
angles a, b and c are all 60o (180÷3)

17. 25/02/2019
90°
60°
70°
26°
55°
90°

18. ANGLES IN A QUADRILATERAL ADD UP TO 360°
25/02/2019
ANGLES IN A QUADRILATERAL ADD UP TO 360°

19. The angles in a quadrilateral add up to 360°
25/02/2019 d c a b
For any quadrilateral,
a + b + c + d = 360°
The angles in a quadrilateral add up to 360°

20. 25/02/2019 Angles TASK 1 EXTENSION 1)
Calculate the value of the missing angles below: j
150º
80º
30º
EXTENSION 1)
Calculate the value of x below:

21. 25/02/2019 Solutions EXTENSION 1) Calculate the value of x below:j
100º
150º
80º
30º
EXTENSION 1)
Calculate the value of x below:
3x + 10 +
2x – 4 +
x + 8 + 28
= 360 6x + 42
= 360 6x
= 318 x
= 53

22. Find the missing angles, giving reasons for your answers
25/02/2019
Find the missing angles, giving reasons for your answers 1) 2)
97°
75°
130° k i j
85°
90°
52°

23. 25/02/2019 Solutions 2) 1) 97° 121° k 75° 130° 52° j 90° i 70° 85° 52°
Vertically opposite angles are equal
Angles in a quadrilateral add to 360°
Angles in a quadrilateral add to 360°

24. BASE ANGLES IN AN ISOSCELES TRIANGLE ARE EQUAL
25/02/2019
BASE ANGLES IN AN ISOSCELES TRIANGLE ARE EQUAL

25. Base angles in an isosceles triangle are equal
25/02/2019
Base angles in an isosceles triangle are equal

26. Calculate angles x and y
25/02/2019
Example a
65o
Calculate angle a b
Angle a = 65o (base angles of an isosceles triangle are equal).
Angle b = 180 –( )
= 180 – 130 = 50o
Calculate angles x and y y
130o x

27. 25/02/2019
650 1) 2) 3) 4)
500
600
500 x
500
800 x x
400 x
200
400 5) 6) 7)
300 8)
450 x
700
700 x x x
600
11)
10) 9) x
12)
600
400
200
350
72.50 x
800
400
300 x x

28. ALTERNATE ANGLES ARE EQUAL, AND CORRESPONDING ANGLES ARE EQUAL
25/02/2019
ALTERNATE ANGLES ARE EQUAL, AND CORRESPONDING ANGLES ARE EQUAL

29. 25/02/2019 Corresponding angles are equal Alternate angles are equal
Interior angles add up to 180° a a a b b b
a = b
a = b
a + b = 180°
Look for an F-shape
Look for a Z-shape
Look for a C- or U-shape

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39. 25/02/2019 x
100o y z
60o

40. 25/02/2019
105o z
55o x y

41. 25/02/2019
58o a b e c g f d
70o h