Question

With the help of a ruler and a compass it is not possible to construct an angle of :

• A. $37.5°$
• B. $40°$
• C. $22.5°$
• D. $67.5°$

Answer 1

The correct option is B

$40°$

Construction of angle with or without rulee or compass.

Explanation for correct option:

$40°=\frac{1}{2}\times 80°$

This is not possible.

$80°$ cannot be constructed with the help of a ruler and a compass.

Hence, it is not possible to construct an angle of $40°$ with the help of a ruler and compass.

Therefore, the correct option is $\mathrm{B}$.

Explanation for incorrect option:

As

$$\begin{gathered} 37.5°=\frac{1}{2}\times 75° \\ 22.5°=\frac{1}{2}\times 45° \\ 67.5°=\frac{1}{2}\times 135° \end{gathered}$$

$75°,45°,135°$ can be constructed with the help of a ruler and a compass.

Therefore, the correct option is Option A, Option C, Option D.

Hence,the correct option is Option $\mathrm{B}$.