7th Maths : Term 1 Unit 5 : Geometry : Construction of special angles without using protractor

**Exercise
5.5**

**1.
Construct the following angles using ruler and compass only.**

**(i)
60° **

**(ii)
120° **

**(iii)
30° **

**(iv)
90°**

**(v)
45° **

**(vi)
150° **

**(vii)
135**

**(i) 60 ^{o}**

**Step 1 :** Draw a line. Mark a point A on it.

**Step 2 :** With A as center draw an arc of convenient radius, to the line
at a point B.

**Step 3 :** With the same radius and B as center draw an arc to cut the
previous arc at C.

**Step 4 :** Join AC. Now ∠BAC is the required angle with the
measure 60°.

** **

**(ii) 120°**

**Step 1 :** Draw a line. Mark a point A on it.

**Step 2 :** With A as center, draw an arc of convenient radius to the line at
a point B.

**Step 3 :** With the same radius and B as center draw an arc to cut the previous
arc at C.

**Step 4 :** With the same radius and C as center draw an arc to cut previous
arc at D.

**Step 5 : **Join AD. Now ∠BAD is the required angle with the
measure 120°.

** **

**(iii) 30°**

**Step 1 :** Draw a line. Mark a point A on it.

**Step 2 :** With A as center, draw an arc of convenient radius to the line
at a point B.

**Step 3 :** With the same radius and B as center draw an arc to cut the
previous arc at C.

**Step 4 :** Join AC. ∠BAC = 60°

**Step 5 :** With B as center, draw an arc of convenient radius in the
interior of ∠BAC.

**Step 6 :** With the same radius and C as center draw an arc to cut the
previous arc at D.

**Step 7 :** Join AD. Now ∠BAD is the required angle with
measure 30°.

** **

**(iv) 90 ^{o}**

**Step 1 :** Draw a line. Mark a point A on it.

**Step 2 : **With A as center, draw an arc of convenient radius to the line at
a point B.

**Step 3 :** With the same radius and B as center draw an arc to cut the previous
arc at C.

**Step 4 :** With the same radius and C as center draw an arc to cut the previous
arc at D.

**Step 5 :** Join AD. ∠BAD = 120°

**Step 6 : **With C as center, draw an arc of convenient radius in the
interior of ∠CAD

**Step 7 : **With the same radius and D as center draw an arc to cut the
previous arc at E.

**Step 8 :** Join AE. Now ∠BAE = 90° is the required angle.

** **

** (v) 45 ^{o}**

**Step 1 :** Draw a line. Mark a point A on it.

**Step 2 :** With A as center, draw an arc of convenient radius to the line at
a point B.

**Step 3 :** With the same radius and B as center draw an arc to cut the previous
arc at C.

**Step 4 :** With the same radius and C as center draw an arc to cut the previous
arc at D.

**Step 5 :** Join AD. ∠BAD = 120°

**Step 6 :** With C as center, draw an arc of convenient radius in the interior
of ∠CAD.

**Step 7 :** With the same radius and D as center draw an arc to cut the previous
arc at E.

**Step 8 :** Join AE. It cuts the previous BCD arc at F ∠B AF = 90°.

**Step 9 :** With B and F as centers draw arcs of convenient radius in the interior
of ∠BAF. They cut G.

**Step 10 :** Join AG Now ∠BAG the required angle with measure
45°.

** **

**(vi) 150°**

**Step 1 :** Draw a line. Mark a point A on it.

**Step 2 :** With A as center, draw an arc of convenient radius to the line at
a point B.

**Step 3 : **With the same radius and B as center draw an arc to cut the previous
arc at C.

**Step 4 :** With the same radius and C as center draw an arc to cut the previous
arc at D.

**Step 5 :** With the same radius and D as center draw an arc to cut the previous
arc at E.

**Step 6 :** With D and E as centers and with the convenient radius draw arcs
in the interior of ∠DAE to cut at F.

**Step 7 :** JoinAF. Now ∠BAF = 150° is the required angle.

** **

**(vii) 135 ^{o }**

**Step 1 :** Draw a line. Mark a point A on it.

**Step 2 :** With A as center, draw an arc of convenient radius to the line
at a point B.

**Step 3 : **With the same radius and B as center draw an arc to cut the
previous arc at C.

**Step 4 :** With the same radius and C as center draw an arc to cut the previous
arc at D.

**Step 5 :** With the same radius and D as center draw an arc to cut the previous
arc at E.

**Step 6 :** With the convenient radius and D and E as centers draw arcs in
the interior of ∠DAE to cut at F.

**Step 7 :** Join AF. It cuts the arc at G. Now GAB = 150°

**Step 8 :** With the convenient radius and G and D as centers draw arcs in
the interior of ∠DAG to cut at H.

**Step 9 :** Join AH. Now ∠BAH = 135° is the required angle.

Tags : Questions with Answers, Solution | Geometry | Term 1 Chapter 5 | 7th Maths , 7th Maths : Term 1 Unit 5 : Geometry

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7th Maths : Term 1 Unit 5 : Geometry : Exercise 5.5 (Construction of special angles without using protractor) | Questions with Answers, Solution | Geometry | Term 1 Chapter 5 | 7th Maths

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