Construction of Angles with Compass

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In the Chapter construction of angles we learn how to construct an angle by compass. It is very easy to construction of angles by compass. To read this chapter you will be able to construct any angle by compass which can be draw by compass. 45 degree angle with compass draw 45 degree angle

First of all we must know, which angle we draw by compass. The number which is multiples of 15, we can easily construct this angles. construction of angles is very important topic for exam.

In this chapter we learn to construct angle with compass.
construction of angles 15 degree angle with compass
construction of angles 30 degree angle with compass
construction of angles 45 degree angle with compass
construction of angles 60 degree angle with compass
construction of angles 75 degree angle with compass
construction of angles 90 degree angle with compass
construction of angles 105 degree angle with compass
construction of angles 120 degree angle with compass
construction of angles 135 degree angle with compass
construction of angles 150 degree angle with compass
construction of angles 165 degree angle with compass
construction of angles 180 degree angle with compass

Required equipment : Ruler (Scale), Pencil, A notebook Compass, Eraser, Sharpener etc   

1. How to draw 15 degree angle
Construction of angles 15 degree angle with compass with main point of Construction 
(a) Draw a line segment 

First of all we draw a line segment using by ruler and pencil (any size).
Screenshot 2B 2528457 2529

(b) Take compass and pencil

Now put pencil in the compass and draw a semicircle using compass.

Screenshot 2B 2528458 2529

(c) Draw the arc

Now put the compass nib on C point then draw a arc. We give this arc name point D.


Screenshot 2B 2528459 2529

(d) From point C and D draw the arc one by one.
from point D
Screenshot 2B 2528471 2529

from point C

Screenshot 2B 2528472 2529

(e) where this two arc intersection each other, we give point E.
(f) Then draw a line from E to A, by using scale and pencil.

in this way we construction an 30 degree angle.

(g) Cut the arc from point F and C.
from point F

Screenshot 2B 2528470 2529

From point C


Screenshot 2B 2528469 2529

(h) where this two arc intersection each other, we give point G.
(i) Then draw a line from G to A, by using scale and pencil.

(j) We get a angle of 15 degree.
Screenshot 2B 2528468 2529

2. How to draw 30 degree angle
30 degree angle with compass
How to draw 30 degree angle

Construction of angles 30 degree angle with compass with main point of Construction 
(a) Draw a line segment 

First of all we draw a line segment using by ruler and pencil (any size).
Screenshot 2B 2528457 2529

(b) Take compass and pencil

Now put pencil in the compass and draw a semicircle using compass.

Screenshot 2B 2528458 2529

(c) Draw the arc

Now put the compass nib on C point then draw a arc. We give this arc name point D.


Screenshot 2B 2528459 2529

(d) From point C and D draw the arc one by one.
from point D
Screenshot 2B 2528471 2529

from point C

Screenshot 2B 2528472 2529

(e) where this two arc intersection each other, we give point E.
(f) Then draw a line from E to A, by using scale and pencil.

in this way we construction an 30 degree angle.
Screenshot 2B 2528474 2529

3. How to draw 45 degree angle
45 degree angle with compass 
How to draw 45 degree angle

Construction of angles 45 degree angle with compass with main point of Construction 
(a) Draw a line segment 

First of all we draw a line segment using by ruler and pencil (any size).
Screenshot 2B 2528457 2529

(b) Take compass and pencil

Now put pencil in the compass and draw a semicircle using compass.

Screenshot 2B 2528458 2529

(c) Draw the arc

Now put the compass nib on C point then draw a arc. We give this arc name point D.


Screenshot 2B 2528459 2529

(d) From point C and D draw the arc one by one.
from point D
Screenshot 2B 2528471 2529

from point C

Screenshot 2B 2528472 2529

(e) where this two arc intersection each other, we give point E.
(f) Then draw a line from E to A, by using scale and pencil.

in this way we construction an 30 degree angle.
Screenshot 2B 2528474 2529

(g) Cut the arc from D and F points.
From D point

Screenshot 2B 2528475 2529

From F point

Screenshot 2B 2528476 2529

(h) Where these two arc intersect each other give point G.
Draw a line from point G to point A.

Screenshot 2B 2528477 2529

in this way we construction an 45 degree angle.

4. How to draw 60 degree angle
60 degree angle with compass 
How to draw 60 degree angle

Construction of angles 60 degree angle with compass with main point of Construction 
(a) Draw a line segment 

First of all we draw a line segment using by ruler and pencil (any size).
Screenshot 2B 2528457 2529

(b) Take compass and pencil

Now put pencil in the compass and draw a semicircle using compass.

Screenshot 2B 2528458 2529

(c) Draw the arc

Now put the compass nib on C point then draw a arc. We give this arc name point D.


Screenshot 2B 2528459 2529

(d) Draw a line from point D to A.

Screenshot 2B 2528478 2529


(e) in this way we construction an 30 degree angle.

5. How to draw 90 degree angle
90 degree angle with compass 
How to draw 90 degree angle

Construction of angles 90 degree angle with compass with main point of Construction 
(a) Draw a line segment 

First of all we draw a line segment using by ruler and pencil (any size).
Screenshot 2B 2528457 2529

(b) Take compass and pencil

Now put pencil in the compass and draw a semicircle using compass.

Screenshot 2B 2528458 2529

(c) Draw the arc

Now put the compass nib on C point then draw a arc. We give this arc name point D.


Screenshot 2B 2528459 2529

(d) Put compass nib on point D and cut a arc E.

Screenshot 2B 2528479 2529
(e) From point D and E cut two arc 
from point E
Screenshot 2B 2528480 2529

from point D

Screenshot 2B 2528481 2529
(f) Where these two arc intersect each other, we give point F.
(g) Draw a line from point G to point A using scale.
Screenshot 2B 2528483 2529

(e) in this way we construction an 30 degree angle.

6. How to draw 75 degree angle
75 degree angle with compass 
How to draw 75 degree angle

Construction of angles 75 degree angle with compass with main point of Construction 
(a) Draw a line segment 

First of all we draw a line segment using by ruler and pencil (any size).
Screenshot 2B 2528457 2529

(b) Take compass and pencil

Now put pencil in the compass and draw a semicircle using compass.

Screenshot 2B 2528458 2529

(c) Draw the arc

Now put the compass nib on C point then draw a arc. We give this arc name point D.


Screenshot 2B 2528459 2529

(d) Put compass nib on point D and cut a arc E.

Screenshot 2B 2528479 2529
(e) From point D and E cut two arc 
from point E
Screenshot 2B 2528480 2529

from point D

Screenshot 2B 2528481 2529
(f) Where these two arc intersect each other, we give point F.
(g) Draw a line from point G to point A using scale.
Screenshot 2B 2528484 2529


(e) in this way we construction an 90 degree angle.

(f) Now put the compass nib on point G and D. And cut two arc.
from point G

Screenshot 2B 2528485 2529

from point D

Screenshot 2B 2528486 2529

(g) Where these both arc intersect each other, give point H

Screenshot 2B 2528487 2529

(h) in this way we construction an 90 degree angle.

7. How to draw 120 degree angle
120 degree angle with compass 
How to draw 120 degree angle

Construction of angles 120 degree angle with compass with main point of Construction 
(a) Draw a line segment 

First of all we draw a line segment using by ruler and pencil (any size).
Screenshot 2B 2528457 2529

(b) Take compass and pencil

Now put pencil in the compass and draw a semicircle using compass.

Screenshot 2B 2528458 2529

(c) Draw the arc

Now put the compass nib on C point then draw a arc. We give this arc name point D.


Screenshot 2B 2528459 2529

(d) Put compass nib on point D and cut a arc E.

Screenshot 2B 2528479 2529

(e) Draw a line from point E to point A.

Screenshot 2B 2528488 2529

(f) in this way we construction an 90 degree angle.


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