Chapter 20

Angles and triangles

20.1 Introduction

Trigonometry is a subject that involves the measurement
of sides and angles of triangles and their relationship to
each other. This chapter involves the measurement of
angles and introduces types of triangle.

20.2 Angular measurement

Anangleis the amount of rotationbetween two straight
lines. Angles may be measured either indegreesor in
radians.
If a circle is divided into 360 equal parts, then each part
is called1degreeand is written as 1 ◦

i.e. 1 revolution= 360 ◦

or 1degreeis

1

360

th of a revolution

Some angles are givenspecial names.

• Any angle between 0◦and 90◦is called anacute
  angle.


• An angle equal to 90◦is called aright angle.


• Any angle between 90◦and 180◦is called anobtuse
  angle.


• Any angle greater than 180◦and less than 360◦is
  called areflex angle.


• An angle of 180◦lies on astraight line.


• If two angles add up to 90◦they are calledcomple-
  mentary angles.


• If two angles add up to 180◦they are calledsupple-
  mentary angles.


• Parallellinesare straightlineswhich arein thesame
  plane and never meet. Such lines are denoted by
  arrows, as in Figure 20.1.
  
  
  • A straight line which crosses two parallel lines is
    called atransversal(seeMNin Figure 20.1).
  
  
  
  

P

R

M

N

g

h e

f

d a

c b Q

S

Figure 20.1

With reference to Figure 20.1,

(a) a=c,b=d, e=gand f=h. Such pairs of

angles are calledvertically opposite angles.

(b) a=e,b=f,c=g andd=h. Such pairs of

angles are calledcorresponding angles.

(c) c=eandb=h. Such pairs of angles are called

alternate angles.

(d) b+e= 180 ◦and c+h= 180 ◦. Such pairs of

angles are calledinterior angles.

20.2.1 Minutesand seconds

One degree may be sub-divided into 60 parts, called

minutes.

i.e. 1degree=60 minutes

which is written as 1 ◦= 60 ′.

DOI: 10.1016/B978-1-85617-697-2.00020-X