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Scan the QR Code or visit https://
P youtu.be/9-X-WDvdfFI to watch the
2 3 video of the construction of an angle
M bisector. Then, explain the rationale of
S the construction steps.

1
60°
Q N R

1 Construct a long arc from 2 With the same distance on 3 Draw a line joining point
Q intersecting both arms the compasses, construct Q and point S. QS is the
QP and QR. Mark the two an arc from M and from N angle bisector of ∠PQR.
points of intersection as M respectively so that the arcs
and N. intersect. Mark the point of
intersection as S.

It is found that ∠PQS = ∠SQR = 30°. We have actually constructed an angle of 30°. CHAPTER
Beginning with the construction of an angle of 60° and the knowledge of an angle
bisector, we can construct other angles accurately using only a pair of compasses and a 8
ruler. For instance,

30°
60° 30° 60° 15°
60° 60° 15°

120° 90° 15°

(a) What is the rationale for the construction of angles of 120°, 90° and 15° as shown above?
(b) Discuss and state other angles that can be constructed by using only a pair of compasses and
a ruler.

Self Practice 8.1g

1. For each of the following angles, explain briefly how you would construct the
angle using only a pair of compasses and a ruler. Then, construct the angle.
(a) 90° (b) 45° (c) 75° (d) 105°

183
Lines and Angles

08 TB Math F1.indd 183 11/10/16 12:17 PM