Page 179 - ICSE Math 6

An angle of 30°

To construct an angle of 30°, follow the steps given below.
Step 1: Using a compass, draw ∠PQR of magnitude 60°.
P S
Step 2: Bisect ∠PQR by drawing ray QS such that ∠PQS = ∠RQS
= 30°. Q R

An angle of 90°
To construct an angle of 90°, follow the steps given below.

Step 1: Draw ray AB with A as its initial point. A B

Step 2: Using a compass, draw an arc of any suitable radius with
centre at A such that it intersects ray AB at C. A
C B

D
Step 3: With C as centre draw an arc of radius AC to intersect
the previously drawn arc at D. A
C B
Step 4: Now, with D as centre, draw an arc of radius AC to E
intersect the arc made in step 2 at E. D
A
Step 5: With centre at D and radius more than half of DE, draw C B
an arc.
Step 6. With the same radius and centre at E, draw an arc
intersecting the arc drawn in step 5 at O. O
E D
Step 7: Join A and O. Thus, ∠OAB is the required angle of
magnitude 90°. A C B

Alternatively:

Step 1: Draw line AB and let O be the point where an angle of A O B
magnitude 90° is to be drawn.

Step 2: Using a compass, draw an arc of suitable radius with C D
centre at O such that it intersects line AB at C and D. A O B

E
Step 3: With centre at C and radius more than half of CD, draw
an arc.
A C O D B

Step 4: With the same radius and centre at D, draw an arc to
intersect the arc drawn in step 3 at E.
E
Step 5: Join O and E. Thus, ∠EOB is the required angle of
magnitude 90°. A C O D B

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