Construction of Angles by using Compass



In construction of angles by using compass we will learn how to construct different angles with the help of ruler and compass.



1. Construction of an Angle of 60° by using Compass

Step of Construction:

(i) Draw a ray OA.

(ii) With O as centre and any suitable radius draw an arc above OA cutting it at a point B.

(iii) With B as centre and the same radius as before, draw another arc to cut the previous arc at C.

(iv) Join OC and produce it to D.




Then ∠AOD = 60°.



2. Construction of an Angle of 120° by using Compass

Step of Construction:

(i) Draw a ray OA.

(ii) With O as centre and any suitable radius draw an arc cutting OA at B.

(iii) With B as centre and the same radius cut the arc at C, then with C as centre and same radius cut the arc at D. Join OD and produce it to E.


Then, ∠AOE = 120°.



3. Construction of an Angle of 30° by using Compass

Step of Construction:

(i) Construction an angle ∠AOD = 60° as shown.

(ii) Draw the bisector OE of ∠AOD.




Then, ∠AOD = 30°.



4. Construction of an Angle of 90° by using Compass

Step of Construction:

(i) Take any ray OA.

(ii) With O as centre and any convenient radius, draw an arc cutting OA at B.

(iii) With B as centre and the same radius, draw an cutting the first arc at C.

(iv) With C as centre and the same radius, cut off an arc cutting again the first arc at D.

(v) With C and D as centre and radius of more than half of CD, draw two arcs cutting each other at E, join OE.


Then, ∠EOA = 90°.



5. Construction of an Angle of 75° by using Compass

Step of Construction:

(i) Take a ray OA.

(ii) With O as centre and any convenient radius, draw an arc cutting OA at C.

(iii) With C as centre and the same radius, draw an cutting the first arc at M.

(iv) With M as centre and the same radius, cut off an arc cutting again the first arc at L.

(v) With L and M as centre and radius of more than half of LM, draw two arcs cutting each other at B, join OB which is making 90°.

(vi) Now with N and M as centres again draw two arcs cutting each other at P.

(vii) Join OP.




Then, ∠POA = 75°.



6. Construction of an Angle of 105° by using Compass

Step of Construction:

(i) After making 90° angle take L and N as centre and draw two arcs cutting each other at S.

(ii) Join SO.




Then, ∠SOA = 105°.



7. Construction of an Angle of 135° by using Compass

Step of Construction:

(i) Construct ∠AOD = 90°

(ii) Produce ∠AO to B.

(iii) Draw OE to bisect ∠DOB.


∠DOE = 45°

∠EOA = 45° + 90° = 135°



Then, ∠EOA = 135°.



8. Construction of an Angle of 150° by using Compass

Step of Construction:

(i) Construct ∠AOC = 120°

(ii) Produce ∠AO to B.

(iii) Draw OD to bisect ∠COB.


Now ∠COD = 30°

Therefore, ∠AOD = 120° + 30° = 150°



Then, ∠AOD = 150°.

Related Links :



Angle.

  • Interior and Exterior of an Angle.
  • Measuring an Angle by a Protractor.
  • Types of Angles.
  • Pairs of Angles.
  • Bisecting an angle.
  • Construction of Angles by using Compass.
  • Worksheet on Angles.
  • Geometry Practice Test on angles.




  • 5th Grade Geometry Page

    5th Grade Math Poblems

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