1. RELATION OF ANGLES

2. A C F B D E 1 2 3 4 1. ADJACENT ANGLES (Sudut yang saling berdekatan) ∠ 2 and ∠ 3 are ADJACENT ANGLES because they have a COMMON RAY FC

3. 3 A C F B D E 1 2 3 4 Can you see other adjacent angles in the figure? 1. ADJACENT ANGLES (Sudut yang saling berdekatan) ∠ EFD and ∠ CFD; common ray FD

4. 4 1. ADJACENT ANGLES (Sudut yang saling berdekatan) ∠ AFB and ∠ CFB; common ray FB A C F B D E 1 2 3 4 Can you see other adjacent angles in the figure?

5. 5 1. ADJACENT ANGLES (Sudut yang saling berdekatan) Are ∠ AFB and ∠ EFD adjacent? ∠ AFB and ∠ EFD are not adjacent because they don’t have a common ray. A C F B D E 1 2 3 4

6. A C F B D E 1 2 3 4 1. ADJACENT ANGLES (Sudut yang saling berdekatan) ∠ 2 and ∠ 3 are ADJACENT ANGLES because they have a COMMON RAY FC Can you see other adjacent angles in the figure? ∠ EFD and ∠ CFD; common ray FD ∠ AFB and ∠ CFB; common ray FB Are ∠ AFB and ∠ EFD adjacent? ∠ AFB and ∠ EFD are not adjacent because they don’t have a common ray.

7. 7 L N M K A C F B D E 2. ANGLE ADDITION (Penjumlahan Sudut) ∠ MNL = ∠ KNL + ∠ MNK ∠ EFB = ∠ EFD + ∠ DFC + ∠ CFB Now may you find measure of ∠ EFB?

8. Two angles that added together are 180°, called: SUPPLEMENTARY ANGLES. 3. SUPPLEMENTARY ANGLES (Dua Sudut yang Saling Berpelurus) R S T 75° T Q S 105° What is supplementary angles? ∠ TSR + ∠ TSQ =180 o Angles ∠ TSR and ∠ TSQ are SUPPLEMENTARY And each one is the SUPPLEMENT of the other. T Q S 105° R S T 75°

9. 9 Example 1: 64° Find the measure of the supplement of the angle below: 180° – 64° = 116° 116° Supplement: AngleSupplement 50 o 130 o 122 o 58 o 103 o 77 o

10. 32X + 108X +10+= 180 40X +20 = 180 40X = 180 – 20 X= 4 ∠ RST = 32X + 10 = 32( )+10 = 128 + 10 = 138° ∠ UST = 180-138 = 42° 4 R S U T 32X + 10 8X + 10 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved Example 2: 40X = 160 X= 160/40 Find the measure of ∠ RST and ∠ UST

11. The ratio of an angle to its supplement is 4 : 5. Find the measure of the angle. Solution Suppose the measure of the angle is 4x so the measure of its supplement is 5x. 4x + 5x = 180 o 9x = 180 o x = 20 o The measure of the angle is 4(20) = 80 o

12. Two angles that added together are 90°, called: COMPLEMENTARY ANGLES. 3. COMPLEMENTARY ANGLES (Dua Sudut yang Saling Berpenyiku) M L K 60° K L N 30° What is complementary angles? ∠ KLM + ∠ NLK =90 o M L K 60° K L N 30° Angles ∠ KLM and ∠ KLN are COMPLEMENTARY And each one is the COMPLEMENT of the other.

13. 13 Find the measure of the COMPLEMENT of the angle below: 90° – 35° = 55° Complement 55° 35° Example 1: AngleComplement 67 o 23 o 33 o 57 o 12 o 78 o 45 o 32’ 44 o 28’

14. 9X + 1020X-7+= 90° 29X +3 = 90 29X = 90 – 3 29X = 87 Both angles are complementary: TRS = 9X+10 = 9( ) + 10 = 27 + 10 TRU =90-37 3 X =87/29 = 3 = 37° = 53° R S T U 9X + 10 20X - 7 FIND: TRS and TRU Example 2:

15. 4. ANGLES FORMING A CIRCLE (Sudut-sudut yang membentuk lingkaran) x°x° y°y° z°z°

16. 3. ANGLES FORMING A CIRCLE (Sudut-sudut yang membentuk lingkaran) x°x° y°y° z°z°

17. 3. ANGLES FORMING A CIRCLE (Sudut-sudut yang membentuk lingkaran) x°x° y°y° z°z° Remember! A full rotation = 360 o It means there are 360 o in a circle. Based on the figure above: x + y + z = 360 o

18. Example 1: Find the value of y on the following figure Solution: 180 o + 58 o + y = 360 o 238 o + y = 360 o y = 360 o – 238 o y =122 o

19. Example 2: Find the value of e on the following figure

20. 4. ANGLES IN A TRIANGLE (Sudut – Sudut Pada Segitiga) x y z In a Triangle, the sum of the angles is 180 o Based on the figure on the left: x + y + z = 180 o

21. Example 1: Find the value of x on the following figure 53 o 71 o x ACD B Solution: ∠A + ∠B + ∠ACB = 180 o 71 o + 53 o + ∠ACB = 180 o 124 o + ∠ACB = 180 o ∠ACB = 180 o – 124 o = 56 o ∠ACB + ∠DCB = 180 o ∠DCB = 180 o – 56 o = 124 o So, x = 124 o