Question

Which of the following angles can not be constructed using straight edge and compass?

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${20}^{\circ }$

Answer 1

The correct option is D ${20}^{\circ }$

${30}^{\circ }$, ${45}^{\circ }$, ${60}^{\circ }$ angles can be constructed using straight edge and compass.
We know, ${20}^{\circ }=\frac{1}{3}{60}^{\circ }$
We know only those things can be constructed whose associated equations have powers of 2 in the exponent.
${20}^{\circ }$ can not be expressed in powers of 2 as its equation cannot be expressed in powers of 2.
$\therefore {20}^{\circ }$ can not be constructed using straight edge and compass.