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# Angles

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### Angles

1. 1. BY : RONALD N S
2. 2.  Full turn : satu putaran penuh(360o) Straight angle : sudut lurus ( 180o) Right angle : sudut siku-siku ( 90o) Acute angle : sudut lancip (0o < x < 90o) Obtuse angle : sudut tumpul (90o< x <180o) Reflex angle : sudut refleks (180o < x < 360o) Protractor : busur derajat Magnitude : besaran, ukuran Longest arm (minute arm) : jarum panjang short arm ( hour arm ) : jarum pendek Complemantary angle : sudut berpenyiku Supplementary angle : sudut berpelurus Vertically opposite : bertolak belakang Intersect : Berpotongan Compasses : Jangka Perpendicular : tegak lurus Bisector : Membagi sudut sama besar
3. 3. Types of AnglesParts of Angle Hexadecimal system Supplementary AnglesLabelling Angles Complementary Angles Clock Angle Problem
4. 4.  The corner point of an angle is called the VERTEX  Two straight lines is called ARMS The angle is the amount of turn between eachBack arm.
5. 5.  There are two main ways to label angles: 1. by giving the angle a name, usually a lower-case letter like a or b, or sometimes a Greek letter like α (alpha) or θ (theta) 2. or by the three letters on the shape that define the angle, with the middle letter being where the angle actually is (its vertex). Example angle "a" is "BAC", and angle "θ" is "BCD"Back
6. 6. BackLook at the picture, and completely the table! B G 2 D 4 C 3 1 F 5 A E H Numbers One letter Three letters 1 A BAC 2 B ABC 3 F GFH 4 G FGH 5 H FHG
7. 7. BackType of Angle DescriptionAcute angle an angle that is less than 90°Right angle an angle that is 90° exactlyObtuse angle an angle that is greater than 90° but less than 180°Straight angle an angle that is 180° exactlyReflex angle an angle that is greater than 180°
8. 8. determine the type of the following angles! Acute Acute Right Acute Acute Obtuse
9. 9. Two Angles are Complementary if they add up to 90 degrees (a Right Angle). These two angles (40° and 50°) are Complementary Angles, because they add up to 90°. If the two angles add to 90°, we say they "Complement" each other. Back
10. 10. Two Angles are Supplementary if they add up to 180 degrees. These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°. If the two angles add to 180°, we say they "Supplement" each other.Back
11. 11. How can you remember which is which? Easy! Think: "C" of Complementary stands for "Corner" (a Right Angle), and "S"of Supplementary stands for "Straight" (180 degrees is a straight line)
12. 12. Remember :1o = 60 ‘ 1‘ = ( 1/ 60 )o1‘ = 60 “ 1“ = ( 1 / 60)‘1o = 3600’’ 1’’ = ( 1/ 3600 )oO read degree‘ read minute“ read second
13. 13. Rewrite 3,15 o into the hexadecimal system!Solution3,15o = 3o + 0,15o = 3o + 0,15 x 1o = 3o + 0,15 x 60’ = 3o + 9’ = 3o9’So, 3,15o = 3o9’
14. 14. Rewrite 3,125o into hexadecimal system!Solution3,125o = 3o + 0,125o = 3o + 0,125 x 1o = 3o + 0,125 x 60’ = 3o + 7,5’ = 3o + 7’ + 0,5’ = 3o+ 7’ + 0,5 x 60’’ = 3o + 7’ + 30’’ = 3o7’30’’
15. 15. Rewrite 19o15’27’’ in degree unit!19o15’27’’ = …..o = 19o + 15’ + 27’’ = 19o + 15 x ( 1/60)o + 27 x ( 1/3600)o = 19o + 0,25o + 0,0075o = 19,2575oSo, 19o15’27’’ = 19,2575o
16. 16. Find the result :a. 15o43’25’’ + 42o52’17’’b. 42o17’52’’ – 25o34’44’’
17. 17. a. 15o43’25’’ 42o52’17’’ + 57o95’42’’ = 58o35’42’’b. 42o17’52’’ 41o77’52’’ 25o34’44’’ - 25o34’44’’ - 16o43’8’’Back
18. 18.  The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute Theminute hand rotates through 360° in 60 minutes or 6° per minute. Back
19. 19. From this statement , we can write :a) Long arm = minute arm 1 hour = 60’ = 360o 1 minute = 360o : 60 = 6ob) Short arm = hour arm 1 hour = 360o : 12 = 30o 1 minute = 30o : 60 = 0,5o
20. 20. What degree is the angle formed by long and short arm of analogue clock at 07.15 am?Solution:Position long arm in number 3Position short arm in number 7So, (7 – 3)x 30o = 4 x 30o = 120oThen Short arm is move = 15 x 0,5o = 7,5oSo, angle formed = 120o + 7,5o = 127,5o
21. 21. Rewrite these questions into hexadecimal system: