Angles and Lines

Standard of Competence:Understand the relation line and line, line and angle, angle and angle, and how to measure its

Basic Competence:1. Determine the relation of two lines, the kind of

angle and its value2. Understand the property of combined angle if

two intersection crossing line or parallel lines intersect with the other line

3. Draw an angle4. Devide an angle

Non-collinear ray

3

What is an angle?

AB

C

Common endpoint called: VERTEX

Non-collinear Ray

INTERIOR

EXTERIOR

EXTE

RIO

R

AB

C

The part of angle:1. Vertex (B)2. Side/Leg/Arm (BA, BC)3. Area of angle :

interior, exterior

Angle is a region forming from two non-collinear rays that has same common endpoint.

Name and Angle Notation

The notation of angle is “ ” followed by the name of the angle∠Name of an angle can be exspresses in 4 ways, that are:

1. Using Greek Letters the Greek letters that usualy used are : α (alpha), β (beta)

θ (tetha), γ (gamma) etc the following angle can be written as “∠ α” or “angle alpha”

2. Using number (natural numbers) the angle on the right can be written as: “∠3” or “angle three”

α3

3. Using three alphabetical lettersto named an angle using three letters, the name of

its vertex should be placed in the middle. So, the name of angle on the left is ∠PQR or ∠RQP. The letters that used to named an angle should capital letters.

4. Using one alphabetical letterthe name of an angle using one letter is same

with the name of its vertex. So, the name of angle on the left is ∠L

RQ

P

ML

K

How many ways may we call this angle?

ABCCBAB

1AB

C

1

Exercises

1. Named of the following angles in 4 different ways.

FE

D

R T

P

θ 1(a) (b)

2. How many angles are on the following figure? What are they?

RQ

SP

Unit of Angles

Sexagesimal System

1o = 60’1’ = 60’’1o = 60 x 60’’ = 3,600’’1’ = (1/60)o1’’ = (1/60)’1’’ = (1/3,600)o

1o read as one degree60’ read as sixty minutes60’’ read as sixty seconds

The unit of angle we can use:Degree of arc (o)Minute of arc ( ’ )Second of arc (’’)

Example 1:1. 4o= ... ’2. 85’’ =... ’ .... ’’3. 40.2o = ... o ... ’4. (3/4)o = ... ’Solving:Remember! 1o = 60’ and 1’ = 60’’1. 4o = 4 x 60’ = 240’2. 85’’ = 1’ 25’’ → 85’’ = 60’’ + 25’’ = 1’ + 25’’3. 40.2o = 40o 12’ → 0.2o = 0.2 x 60’ = 12’4. (3/4)o = 45’ → (3/4)o = (3/4) x 60’ = 45’

Example:1. 29o16’20’’ + 20o56’58’’= ....2. 40o06’35’’ + 29o56’57’’= ....Solving:Remember! 1o = 60’ and 1’ = 60’’1. 29o16’20’’ + 20o56’58’’= ....29o 16’ 20’’ 20o 56’ 58’’

49o 72’ 78’’ = 49o + (1o + 12’) + (1’ + 18’’) = 50o13’18’’

Exercises

1. 6’= ... ’’2. 96’ = ... o .... ’3. 52.3o = ... o ... ’4. 46.6’ = ... ’ ... ’’5. 25o 24’= ... O6. 78o 115’ = ... o .... ’7. 25o 76’ 88’’ = ...o ....’ ....’’8. 35o 46’ 28’’ + 45o 38’ 50’’ = ...o ....’ ....’’9. 43o 12’ 26’’ + 18o 38’ 30’’ = ...o ....’ ....’’10.63o 23’ 12’’ – 32o 48’ 52’’ = ...o ....’ ....’’