Question

How will you construct a ${45^o}$ angle?

Answer 1

Hint – In this particular question as this is a construction base question so the given 45 degree is written as (90/2) degree, so first construct the 90 degree and then take the bisector of the 90 degree angle with the baseline to reach the solution of the question so use these concepts to get on right track.

Complete step-by-step answer:
As this a question based on construction so it follows step by step procedure, the following steps which are included in the construction are as follows:
$\left( i \right)$ First draw a straight line AB which acts as a base, as shown in the below figure.

$\left( {ii} \right)$ Now take a compass and point it on A (fix this point) and draw an arc with an appropriate length by another hand or by the free hand of the compass as shown in the below figure.

$\left( {iii} \right)$ Now that same appropriate length taken in step 2, and this time the fix point is on C, and make an arc by the free hand on the arc which is created in step 2, it cut the previous arc at some point name it as D point and then apply the fix point of the compass at point D and then make another arc on the previous arc created in step 2 it again cut that arc at a particular point name it point E as shown in the below figure.

$\left( {iv} \right)$ Now put the fix point on point D and make an arc above the big arc with an appropriate distance taken in compass, now put the fix point of the compass on point E and make an arc with same distance and make an arc with cut the previous arc at a particular point name it as F join this F point and A point as shown in the below figure, it cuts the big arc at point G, so the this line make with the base is 90 degree as shown in the figure.

$\left( v \right)$ Now make the arc from the point G and C respectively which cuts each other at point H as shown in the figure which is the bisector of the 90 degree from the base AB, now join the point H and the A point, so this line AH make the angle with the base AB, 45 degree as shown in the below figure.
$ \Rightarrow \angle HAB = {45^o}$
 

So this is the required construction.

Note – Whenever we face such types of questions the key concept we have to remember is that the above following steps are the basis of the construction so always remember these steps, these steps will help us a lot in constructing the 45 degree angle as above so we will get the required answer.