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Construction of Angles of Measure 60°, 90°, 120°
Construction of an angle of 60°:
Steps of construction:
C
1. Draw a ray AB.
2. Taking A as centre with radius more than half of AB, draw an arc E
cutting AB at D.
3. Taking D as centre, draw another arc of the same radius cutting
the previous arc at E.
4. Join AE and extend it to C.
A D B
Thus, ∠BAC is the required angle of 60°.
Construction of an angle of 90°:
Steps of construction:
1. Draw a ray OA.
2. Taking O as the centre with radius more than half of ray OA, draw an arc which cuts OA at C.
3. Taking C as the centre, draw another arc of the same radius as in step
2 to cut the previous arc at D. B
4. Taking D as the centre, draw another arc of the same radius as before F
to cut the first arc obtained in step 2 at E.
E D
5. Now, draw two arcs of the same radius as above by taking D and E
as centres, respectively, so that they intersect at F.

6. Join OF and extend it to B. O C A
Thus, ∠AOB is the required angle of 90°.
Construction of an angle of 120°: Maths Talk
Steps of construction: Can you explain why the angle
1. Draw a ray OA. constructed in this way measures 90°?
2. Taking O as centre, draw an arc with radius more than half of ray OA to cut OA at C.
3. Taking C as the centre, draw an arc of the same radius as in step 2 B
to cut the previous arc at D.
4. Similarly, taking D as the centre draw another arc of the same E D
radius as before to cut the first arc at E.

5. Join OE and extend it to B.
Thus, ∠AOB is the required angle of 120°. O C A
Construction of angles of 30° and 45°
We can construct angles of 30° and 45° by the construction of the angle bisector of angles of 60°
and 90°, respectively.

D
B Think and Answer
B
E
C How will you construct an
angle of 15°?

O A O A
∠AOC = ∠BOC = 30° ∠AOB = ∠BOD = 45°

341 Construction of Basic Geometrical Shapes