Understanding Engineering Mathematics

SoAP=90 cm andPB=60 cm.

APB

x

x − 30

30

5.2.2 Intersecting and parallel lines and angular measurement
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143 160➤

Given two intersecting lines, in a plane, theanglebetween them is the amount of rota-
tion required to superimpose one on the other, measured in some conventional (usually
anticlockwise as shown) direction. We denote the angle by AOB(see Figure 5.10).

A

∠AOB

B

O

Figure 5.10Definition of angle.

Sometimes, if it is helpful, we use an arc to denote an angle, but usually we try to
avoid cluttering up a diagram. The angle is usually measured indegrees, with one degree,
denoted 1°, being 1/360 of a full rotation. Alternatively, we can measure angles inradians.
One radian (1 rad or 1cfor ‘circular measure’) is essentially the angle subtended at the
centre of a circle by an arc of length equal to the radius. If this rather obtruse definition
does little for you, just note that the number of radians in a complete revolution will be
the number of times that the radius divides the circumference, which is simply 2π.So
there are 2πradians in a complete revolution and therefore

2 πradians=360 degrees= 360 °

Since 180°is half a full rotation, it follows that angles which add together to make 180°
form a straight line – such angles are calledsupplementary.

O

A

C

180 ° B

Figure 5.11Supplementary anglesAOCandCOB.