Question

Ted has a geometry box. Out of several equipments that are there, there are 2 set squares. He was thinking about the angles that could be constructed using those 2 set squares. He took 4 examples to work on which are given in the options below. Which of the following is impossible to draw using the given set squares?

• A. 45°
• B. 60°
• C. 95°
• D. 105°

Answer 1

The correct option is C

95°

We can make ${30}^{\circ },{60}^{\circ }$ and ${105}^{\circ }$ angles by the methods as shown in the figure above. But ${95}^{\circ }$ angle can't be constructed using the $2$ set squares. This is because we can break ${95}^{\circ }$ as $({45}^{\circ }+{50}^{\circ }),({30}^{\circ }+{65}^{\circ }),({60}^{\circ }+{35}^{\circ }),({90}^{\circ }+{15}^{\circ })$ or $({75}^{\circ }+{20}^{\circ })$. In all the cases, we can construct one of the pair of angles. We can't construct both.