Page 180 - ICSE Math 6

An angle of 45°

To construct an angle of 45°, follow the steps given below.
Step 1: Using a compass, draw ∠PQR of magnitude 90°. P S

Step 2: Bisect ∠PQR by drawing ray QS such that ∠PQS = ∠RQS
= 45°.
Q R
An angle of 120°

To construct an angle of 120°, 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 suitable radius with
centre at A to intersect ray AB at C. A
C B

Step 3: With the same radius and C as centre, draw an arc which D
intersects the previous arc at D.
A C B

E D
Step 4: With the same radius and D as centre, draw an arc which
intersects the arc made in step 2 at E. A C B

E D
Step 5: Join A and E. Thus, ∠EAB is the required angle of
magnitude 120°. A C B

An angle of 135°

To construct an angle of 135°, follow the steps given below.
Step 1: Using a compass, draw ∠ABC of magnitude equal to
90°. E A

Step 2: Bisect ∠ABD by drawing ray BE.
As, ∠ABE = ∠DBE = 45°. So, ∠EBC = 45° + 90° = 135°. D B C

To Draw a Perpendicular to a Line

From a point not on the line P

Let AB is a line and P is a point, not on it.
To draw a perpendicular to line AB from point P, follow the steps A B
given below.

Step 1: With P as centre, draw an arc of suitable radius to intersect P
line AB at C and D.

A C D B

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