1. Circle Theorems Angles subtended from the same arc.
Angles subtended from the same arc are equal.

2. Example
Find the lettered angles for each of the following
50 a
(i)

3. (ii)
18 b

4. (iii)
22 c
72 d e

5. (iv)
90 g
65

6. (v)
105 h i
24

7. (vi)
84 x y
30

8. (iii) h
123
105 k i

9. Angle subtended at the centre
The angle subtended at the centre from an arc is double the angle at the circumference.

10. Find the lettered angles for each of the following
Circle Theorems
Example
Find the lettered angles for each of the following
(i) m
84

11. (ii) n
76

12. (iii) y
230

13. (iv) w
68

14. (v) c
82 a b

15. (vi) q
24 p r

16. (ii)
120 x y

17. (v) 46 t v u

18. Angles in a semi-circle
90
The largest angle in a semi-circle will always be 90

19. Example
Calculate the size of the lettered angle for each of the following:
(i)
28 a b

20. (ii) a
135 b

21. (iii) k j 27

22. (iv)
167
108 m n

23. Example Find the lettered angles for each of the following:
12 p