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Question

Given an angle θ, which of the following angles cannot be obtained by using the method of construction of angle bisectors?
  1. θ2
  2. θ4
  3. θ6
  4. θ8

A
θ4
B
θ6
C
θ2
D
θ8
Solution
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Angle bisector is bisects or divide the angle into two equal parts.
If θ is given, we can find θ2 by bisecting θ into two parts and θ2 will be half of θ.
By construting angle bisector of angle θ2, we can get θ4 which is half of θ2.
And then again bisecting θ4, we can get the angle θ8 which is half of θ4.
Hence, by using method of construction of angle bisectors we can find θ2,θ4,θ8 but not θ6 as it is half of θ3 which can't be determined by angle bisector.
Hence, the answer is θ6.

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