ANGLESBY : RONALD N S

GLOSSARY 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

CONTENT

Parts of Angle

Supplementary Angles

Complementary Angles

Types of Angles

Labelling Angles

Hexadecimal system

Clock Angle Problem

PARTS OF ANGLES The corner point of

an angle is called the VERTEX

Two straight lines is called ARMS

The angle is the amount of turn between each arm.Back

LABELLING ANGLES 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

EXERCISE…Look at the picture, and completely the

table!

AH

F

D

C

E

B G

1

4

5

3

2

Numbers One letter Three letters

1 A BAC

2

3

4

5

Back

B

F

G

H

ABC

GFH

FGH

FHG

TYPES OF ANGLESType of Angle

Description

Acute angle an angle that is less than 90°

Right angle an angle that is 90° exactly

Obtuse angle

an angle that is greater than 90° but less than 180°

Straight angle

an angle that is 180° exactly

Reflex angle an angle that is greater than 180°

Back

EXERCISE…determine the type of the following

angles!

Acute

Obtuse

AcuteAcute

RightAcute

COMPLEMENTARY ANGLES

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.

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SUPPLEMENTARY ANGLES

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

COMPLEMENTARY VS SUPPLEMENTARY

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)

HEXADECIMAL SYSTEMRemember :1o = 60 ‘ 1‘ = ( 1/ 60 )o 1‘ = 60 “ 1“ = ( 1 / 60)‘1o = 3600’’ 1’’ = ( 1/ 3600 )o

O read degree‘ read minute“ read second

EXAMPLE 1Rewrite 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’

EXAMPLE 2Rewrite 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’’

EXAMPLE 3Rewrite 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

= 19,2575o

So, 19o15’27’’ = 19,2575o

ADDING & SUBSTRACTING Find the result :a. 15o43’25’’ + 42o52’17’’b. 42o17’52’’ – 25o34’44’’

SOLUTION…a. 15o43’25’’

42o52’17’’ +57o95’42’’ = 58o35’42’’

b. 42o17’52’’ 41o77’52’’25o34’44’’ - 25o34’44’’ -

16o43’8’’

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CLOCK ANGLE PROBLEM

The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute

The minute hand rotates through 360° in 60 minutes or 6° per minute.

Back

From this statement , we can write :a) Long arm = minute arm

1 hour = 60’ = 360o

1 minute = 360o : 60 = 6o

b) Short arm = hour arm1 hour = 360o : 12 = 30o 1 minute = 30o : 60 = 0,5o

EXAMPLE…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 = 120o

Then Short arm is move = 15 x 0,5o

= 7,5o

So, angle formed = 120o + 7,5o = 127,5o

MAGNITUDE OF ANGLES

SMALL TESTRewrite these questions into hexadecimal

system: