Question

Which of the following angles can be constructed with the help of simply a ruler and a pair of compass?

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

Answer 1

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

${42.5}^{\circ }=\frac{1}{2}\times {85}^{\circ }$
since ${85}^{\circ }$ 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.