Question

Draw an angle of measure ${30}^{\circ }$and construct its bisector.

Answer 1

Hint: To draw an angle of ${30}^{\circ }$and its bisector, we will be following steps of construction of these angles. First, we will draw a baseline and on that we will construct both the angles.

Complete step-by-step answer:
First we will draw the angle of ${30}^{\circ }$on a line AB. Steps to make an angle of ${30}^{\circ }$are shown below:

Step I: We will first draw a line segment AB of any length and then we will extend it on both sides.
Step II: Now, we will draw a semicircle of the radius = AB on this line.
Step III: Now, with the same radius, we will cut an arc on the semicircle drawn. The intersection point is named C. The angle CAB will have measure of ${60}^{\circ }$.
Step IV: From C, we will cut an arc of equal radius and from B, we will cut the arc on the arc which is already cut from C.
Step V: Now, we will join the point A to the arcs. The point at which this line intersects the line is named D. The angle $$\mathrm{D}\mathrm{A}\mathrm{B}={30}^{\circ }$$.

Now, we will draw the angle bisector of${30}^{\circ }$. Angle bisector is a line which divides the angle into two equal halves. Now, to draw the angle bisector of${30}^{\circ }$(which is an angle of ${15}^{\circ }$), we will first draw an angle of ${30}^{\circ }$with the help of steps for the construction of ${30}^{\circ }$. So, let us draw ${30}^{\circ }$angle first on the line segment AB.

Now from B and C, we will cut arcs of the radius same as the radius of the semicircle, and then we will join the intersection point to A. The point at which the line intersects semicircle is named D. The measure of angle $$\mathrm{D}\mathrm{A}\mathrm{B}={15}^{\circ }$$. It is shown in the figure below:
 

Note: To check whether the angle bisector drawn by us is correct or not, we will take radius equal to DB and then cut the arc on line AE from point D. If this arc lies on the semicircle then the angle bisector drawn by us is correct.