Question

can be constructed with the help of just a ruler and a pair of compasses.

• A. ${42.5}^{\circ }$
• B. ${40}^{\circ }$
• C. ${67.5}^{\circ }$
• D. ${55}^{\circ }$

Answer 1

The correct option is C ${67.5}^{\circ }$

${42.5}^{\circ }=\frac{1}{2}\times {85}^{\circ }$ and ${85}^{\circ }$ cannot be constructed
${40}^{\circ }=\frac{1}{2}\times {80}^{\circ }$ and ${80}^{\circ }$ cannot be constructed
${67.5}^{\circ }=\frac{{135}^{\circ }}{2}=\frac{1}{2}({90}^{\circ }+{45}^{\circ })$ can be constructed
${55}^{\circ }=\frac{1}{2}\left(110\right)$ and ${110}^{\circ }$ cannot be constructed.