Draw $\angle AOB=60{}^\circ $ using a protractor. Now, using a compass and ruler construct $\angle XOY=\angle AOB$ .

Hint: Firstly, we have to draw a ray OB. With O as centre, we have to draw an angle $60{}^\circ $ using the protractor. Therefore, we will get $\angle AOB=60{}^\circ $ . We have to draw an arc on OA and OB with any radius and O as centre. Let us denote C and D as the points that cut OA and OB respectively. Now, we have to draw a ray OY from O. Then, we have to take the measure of arc CD with O as centre using a compass and draw an arc of same length such that it cuts OY at P. Now, with the CD measure, cut an arc. We will denote this point as Q. We will get $CD=PQ$ . Finally, we have to extend the ray O through Q to get a ray OX.

Complete step by step answer:
We have to draw $\angle XOY=\angle AOB$ . We can see that the vertex O is common. So, we have to draw $\angle XOY$ along with $\angle AOB$ .
Firstly, we have to draw a ray OB.

With O as centre, we have to draw an angle $60{}^\circ $ using protractor. Therefore, we will get $\angle AOB=60{}^\circ $ .

Now, we have to draw an arc on OA and OB with any radius and O as centre. Let us denote C and D as the points that cut OA and OB respectively.

Now, we have to draw a ray OY from O.

We have to take the measure of arc CD with O as centre using a compass and draw an arc of same length such that it cuts OY at P.

Now, with the CD measure, cut an arc. We will denote this point as Q. We will get $CD=PQ$ .

We have to extend the ray O through Q to get a ray OX.

Hence, we constructed $\angle XOY=\angle AOB$ .

Note: Students must know to use a protractor, measure and draw angles using it. We have to draw $\angle XOY$ by extending $\angle AOB$ . Students should always consider the arc length CD to draw PQ. All these constructions must be done with O as center.