Question

We cannot construct an angle of by using compass and ruler only.

• A. ${90}^{\circ }$
• B. ${45}^{\circ }$
• C. ${15}^{\circ }$
• D. ${20}^{\circ }$

Answer 1

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

${90}^{\circ }$ can be drawn by bisecting ${180}^{\circ }$, which is a straight line. ${45}^{\circ }$ can be drawn by bisecting ${90}^{\circ }$.
${15}^{\circ }$ can be drawn by bisecting ${60}^{\circ }$ twice.
If we look at the values of angles that can be constructed by a compass, they are multiples of ${15}^{\circ }$ and 20 is not a multiple of 15.
Therefore, ${20}^{\circ }$ cannot be constructed using compass and ruler.