Question

Construct an angle of measure $150{}^\circ $ using only set squares.

Answer 1

Hint:Place the $90{}^\circ $ vertex of any of the set-square and make angle of 90° by drawing the rays BD and BC.  Then, place the $60{}^\circ $ vertex of the 60 - 30 set square on the ray BD and draw the ray BA. $\angle ABC=150{}^\circ $ is the required angle.

Complete step-by-step answer:
In this question, we have to construct an angle of measure $150{}^\circ $ using only set squares.
First, let us see what a set square is.
A set square or triangle is an object used in engineering and technical drawing, with the aim of providing a straightedge at a right angle or other particular planar angle to a baseline. The simplest form of set square is a triangular piece of transparent plastic with the centre removed.
There are two types of set squares and they are named according to the angles present on each.
First is 60 – 30 set square which is a right angled triangle with angles $90{}^\circ ,60{}^\circ ,\text{ and 30}{}^\circ $.
The other one is 45 set square which is a right angled triangle with angles $90{}^\circ ,45{}^\circ ,\text{ and 45}{}^\circ $.
Now, using these we have to construct an angle of $150{}^\circ $.
Place the $90{}^\circ $ vertex of any of the set-square and make angle of 90° by drawing the rays BD and BC as shown in the figure below.

Then, place the $60{}^\circ $ vertex of the 60 - 30 set square on the ray BD as shown in the figure below and draw the ray BA.

The angle ABC so formed is equal to $150{}^\circ $.
Therefore, $\angle ABC=150{}^\circ $

Note: In this question, it is very important to know what a set square is and what are the angles present on each. The set squares have angles $90{}^\circ ,45{}^\circ ,60{}^\circ ,\text{ and 30}{}^\circ $. So, we can construct any angle which is a combination of two or more of these angles.