Question

Which of the following angles 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

Answer: (C)

${42.5}^{\circ }=\frac{1}{2}\times {85}^{\circ }$ and ${85}^{\circ }$ cannot be constructed simply by using a compass and a ruler.

${40}^{\circ }=\frac{1}{2}\times {80}^{\circ }$ and ${80}^{\circ }$ cannot be constructed simply by using a compass and a ruler.

${67.5}^{\circ }=\frac{{135}^{\circ }}{2}=\frac{1}{2}({90}^{\circ }+{45}^{\circ })$
$({90}^{\circ },{45}^{\circ })$ can be constructed by using a compass and a ruler.

${55}^{\circ }=\frac{1}{2}\left(110\right)$ and ${110}^{\circ }$ cannot be constructed by using a compass and a ruler.