Question

Draw an angle of ${{70}^{\circ }}$ using a protractor. Bisect this angle using a compass and ruler.

Answer 1

Hint:First of all, we have to draw an angle of ${{70}^{\circ }}$ by using a protractor which is pretty simple, because you just have to place the protractor on the paper and mark a dot on the 0 markings of the protractor and call it as O then from this point draw a ray. After that mark a dot adjacent to the angle ${{70}^{\circ }}$ and then join O to this point. Now, to bisect this angle using a compass, but the needle of the compass on the vertex O of the angle and open the compass then span an arc in such a way that it will intersect the two arms of the angle in two distinct points. Then put your compass on one of the intersections of the arc and the arms of the angle then open the compass a little more than half of the angle and make an arc similarly, cut the before arc by placing the needle of the compass on the other intersection of the arc and the arms. Then join the intersection of the arcs and the vertex O.

Complete step by step answer:
First of all, we are going to draw an angle of ${{70}^{\circ }}$ by using a protractor. So, we are drawing a ray in which the point of the ray coincides with the 0 markings of the protractor as follows:

Now, using the protractor we will draw an angle of ${{70}^{\circ }}$ by placing the protractor on the ray OA in such a way that 0 markings of the protractor will coincide with the point O of the ray then we will mark the point adjacent to ${{70}^{\circ }}$ and name it as B.

From the above figure, you can see that angle AOB is ${{70}^{\circ }}$.
Now, we are going to bisect this angle by putting the needle of the compass on the vertex A and open the compass a little then span an arc in such a way that it will cut the rays OA and OB in two different points.

Now, place the needle of the compass on the point F and open the compass with a radius just greater than half of the angle ${{70}^{\circ }}$ and span a small arc inside the area of the angle AOB.

Don’t change the radius of the compass and with this radius draw another arc by putting the needle of the compass on point G and then name the intersection of the two arcs as E.

Now, we are going to draw a ray from point O in such a way that it passes through point E.

As you can see that we have bisected the angle ${{70}^{\circ }}$ and $\angle EOA=\angle BOE={{35}^{\circ }}$.

Hence, we have drawn an angle ${{70}^{\circ }}$ and the bisector of angle ${{70}^{\circ }}$which is equal to ${{35}^{\circ }}$.
Note:
 You can check the bisector of angle ${{70}^{\circ }}$ by placing the protractor on OA and see whether the point E is coinciding with the angle ${{35}^{\circ }}$ on the protractor. If it is coinciding that means you have drawn the correct angle bisector of ${{70}^{\circ }}$. The other thing to keep in mind is that while using the protractor, always use the angles which are written on the lower arc of the protractor. There are two arcs demarcated in the protractor so you have to consider the lower arc of angles, not the upper one.