Construct angles of the following measures using ruler and compasses. ${30^0}$

Hint – In this question consider an arm say AB and place the sharp end of the compass at one of the end points, after drawing an arc of any length that cut’s this arm. Now the distance between the pencil and the compass need not to be changed while making another arc for the angle bisector from the point where the arc form cuts the arm that is point R.

Complete step-by-step answer:

Steps of constructing 30⁰ using ruler and compasses.
Step – 1 Draw an arm AB.
Step – 2 Place the point of the compass at A and draw an arc that cuts the line AB at V.
Step – 3 Now place the compass at point V with the same distance as the previous arc cut the arc drawn in step2 at point M.
Step – 4 With the point of the compass still at V make an arc between M and V as shown in figure.
Step – 5 Now place the compass at M with the same distance as the previous arc cut the arc drawn in step 4 at point R.
Step – 6 Now join A to R. so the angle formed RAB is 30⁰.
$ \Rightarrow \angle RAB = {30^0}$.
So this is the required procedure of constructing angle 30⁰ using ruler and compasses.

Note – ${30^0}$ is the angle bisector for ${60^0}$, after performing all the steps till the points where we have obtained point M (see figure) if point A is directly connected to point M then it makes an angle${60^0}$. If after all the steps completed to make ${30^0}$, the steps are further repeated then the angle bisector for ${30^0}$that is ${15^0}$could also be obtained, so there lies a symmetry which we need to understand.