Basic Engineering Mathematics, Fifth Edition

168 Basic Engineering Mathematics

Thus, 49 ◦is an acute angle.

(c) An angle equal to 90◦is called aright angle.

(d) Any angle greater than 180◦and less than 360◦is

called a reflex angle.

Thus, 245 ◦is a reflex angle.

Problem 8. Find the angle complementary to

48 ◦ 39 ′

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

mentary angles. Hence,the angle complementary to

48 ◦ 39 ′is

90 ◦− 48 ◦ 39 ′= 41 ◦ 21 ′

Problem 9. Find the angle supplementary to

74 ◦ 25 ′

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

mentary angles. Hence,the angle supplementary to

74 ◦ 25 ′is

180 ◦− 74 ◦ 25 ′= 105 ◦ 35 ′

Problem 10. Evaluate angleθin each of the

diagrams shown in Figure 20.3

(a) (b)

418

^538448



Figure 20.3

(a) The symbol shown in Figure 20.4 is called aright

angleand it equals 90◦.

Figure 20.4

Hence, from Figure 20.3(a),

θ+ 41 ◦= 90 ◦

from which, θ= 90 ◦− 41 ◦= 49 ◦

(b) An angle of 180◦lies on a straight line.

Hence, from Figure 20.3(b),

180 ◦= 53 ◦+θ+ 44 ◦

from which, θ= 180 ◦− 53 ◦− 44 ◦= 83 ◦

Problem 11. Evaluate angleθin the diagram

shown in Figure 20.5

39 

58 

64 

108 



Figure 20.5

There are 360◦in a complete revolution of a circle.

Thus, 360◦= 58 ◦+ 108 ◦+ 64 ◦+ 39 ◦+θ

fromwhich, θ= 360 ◦− 58 ◦− 108 ◦− 64 ◦− 39 ◦= 91 ◦

Problem 12. Two straight linesABandCD

intersect at 0. If∠AOCis 43◦,find∠AOD,

∠DOBand∠BOC

From Figure 20.6,∠AODis supplementary to∠AOC.

Hence,∠AOD= 180 ◦− 43 ◦= 137 ◦.

When twostraight linesintersect, the verticallyopposite

angles are equal.

Hence, ∠DOB= 43 ◦and∠BOC 137 ◦

A D

C B

(^4380)
Figure 20.6