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**Construction of Angles**

In construction of angles here we are going to learn on how
to construct the different angles by using of scale, pencil and compass. We can
construct the angles 60°, 120°, 30°, 90°, 45°, 135°, 75°, 105° etc. by using
the compass. Let’s learn them.

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**Construction of an angle 60°**

**Steps:**

1. Draw a line segment AB.

2. Draw an arc of any size with the centre at the
point B, so that it cuts AB at point D.

3. Cut the same size of the previous arc at E from
the point D.

4. Join the points E and B to meet C as shown in
the figure.

5. Then ∠ABC = 60°.

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**Construction of an angle 120°**

**Steps:**

1. Draw a line segment AB.

2. Draw an arc of any size with the centre at B
which cuts AB at C.

3. Cut the same size of the previous arc at the
point D from the point C.

4. Again cut the same arc at E from the point D.

5. Join the points E and B to meet F as shown in
the figure.

6. Then, ∠ABF = 120°.

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**Construction of an angle 30°**

**Steps:**

1. Construct an angle of 60° as before.

2. Draw an arc from the point D and E which
intersect at the point F as shown in the figure.

3. Join the points B and F. Then BF bisects the ∠ABC.

4. Then, ∠ABF = 30°.

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**Construction of an angle 90°**

**Steps:**

1. Construct the angles 60° and 120° as before.

2. Draw same arcs from C and D so that the two arcs
intersect at E as shown in the figure.

3. Join the points O and E.

4. Then, ∠AOE = 90°.

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**Construction of an angle 45°**

**Steps:**

1. Construct an angle of 90° as above.

2. Draw same arcs from B and E so that they
intersect at F.

3. Join the points F and O as shown in the figure.

4. Then, ∠FOA = 45°.

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**Construction of an angle 135°**

**Steps:**

1. Construct an angle of 90° as above.

2. Draw same arcs from F and E so that they
inersect at G.

3. Join the points G and O as shown in the figure.

4. Then, ∠AOG = 135°.

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**Construction of an angle 75°**

**Steps:**

1. Construct an angle 90° as before.

2. Draw same arcs from D and F so that they
intersect at the point G.

3. Join the points G and B as shown in the figure.

4. Then, ∠ABG = 90°.

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**Construction of an angle 105°**

**Steps:**

1. Construct an angle of 90° as before.

2. Draw same arcs from U and T so that they
intersect at the point V.

3. Join the points Q and V as shown in the figure.

4. Then, ∠AQV = 105°.

*You can comment your questions or problems regarding the construction of angles by using compass here.*

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