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Construction 11.3 :
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To construct an angle of 60° at the initial Point of a given ray.

Let us take a ray AB with initial Point A.

We want to construct a ray AC such that ∠CAB = 60°

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Steps of Construction
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:
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- Taking A as centre and some radius, draw an arc of a circle, which intersects AB at Point D.
- Taking D as Centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point E.
- Draw the ray AC Passing through E.

Thus, ∠CAB is the required angle of 60°

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Justification
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We need to prove ∠ CAB = 60°

Join DE.

Since arc AD = Arc AE

and using same radius, we drew arc DE

Thus, their radius will be the same

∴ AE = AD = DE

Therefore, ∆ EAD is an equilateral triangle

∴ ∠EAD = 60°

⇒ ∠CAB = 60°.

Hence justified