Question

Which of the following angles cannot be constructed using ruler and compass only?
(a) $22\frac{1}{2}°$
(b) $15°$
(c) $52\frac{1}{2}°$
(d) $32\frac{1}{2}°$

Answer 1

Since, the angle $22\frac{1}{2}°$ is half of ${45}^{\circ }$ is multiple of $15$.

Similar way, $15°$ is also multiple of $15$.

Similar, way $52\frac{1}{2}°$ is half of ${105}^{\circ }$ is again multiple of $15$.

Where as $32\frac{1}{2}°$ is half of ${65}^{\circ }$ is not multiple of $15$.

So, the angle $32\frac{1}{2}°$​ cannot be constructed using ruler and compass.

Hence, the correct the option is ($d$)