Question

Given an angle $\theta$, which of the following angles cannot be obtained by using the method of construction of angle bisectors?

• A. $\frac{\theta }{2}$
• B. $\frac{\theta }{4}$
• C. $\frac{\theta }{6}$
• D. $\frac{\theta }{8}$

Answer 1

The correct option is C $\frac{\theta }{6}$

Angle bisector is bisects or divide the angle into two equal parts.

If $\theta$ is given, we can find $\frac{\theta }{2}$ by bisecting $\theta$ into two parts and $\frac{\theta }{2}$ will be half of $\theta$.

By construting angle bisector of angle $\frac{\theta }{2}$, we can get $\frac{\theta }{4}$ which is half of $\frac{\theta }{2}$.

And then again bisecting $\frac{\theta }{4}$, we can get the angle $\frac{\theta }{8}$ which is half of $\frac{\theta }{4}$.

Hence, by using method of construction of angle bisectors we can find $\frac{\theta }{2},\frac{\theta }{4},\frac{\theta }{8}$ but not $\frac{\theta }{6}$ as it is half of $\frac{\theta }{3}$ which can't be determined by angle bisector.

Hence, the answer is $\frac{\theta }{6}$.