Question

Construct an angle of $${75}^{\circ }$$ and bisect it.

Answer 1

Hint: “Construction” is related to the geometric part in Mathematics. Geometry means the study of size, shapes, position angles, lines and dimensions. Here, we have to construct an angle of $${75}^{\circ }$$ and then bisect this angle. This is a pure form of geometry, no numbers involved at all. We will need a pencil, a ruler and a compass to complete the given question.

Complete step-by-step answer:
To construct an angle of $${75}^{\circ }$$ , we need to follow the mentioned below steps:
Step 1: Draw a line $$OP$$ as a base of angle.
Step 2: Using compass, draw an arc of any radius taking $$O$$ as centre intersecting $$OP$$ at point $$A$$ .
Step 3: Taking the compass at the same length, draw an arc with $$A$$ as centre, on the arc intersecting at point $$B$$ .
Step 4: $$$$ Taking the same length of compass, draw again an arc taking $$B$$ as centre intersecting the arc at point $$C$$ .
Step 5: Taking any radius, draw two arcs with $$B$$ and $$C$$ as centres such that both the arcs intersect each other at $$D$$
Step 6: Join $$OD$$ such that the line $$OD$$ intersects the arc at point $$E$$ . $$\mathrm{\angle }DOP$$ is the angle measuring $${90}^{\circ }$$
Step 7: Now, take $$E$$ and $$B$$ as centres and draw two arcs of any length such that both the arcs intersect each other at point $$F$$ .
Step 8: Join point $$F$$ and point $$O$$ such that the line $$OF$$ intersects the arc at point $$L$$ . $$\mathrm{\angle }FOA$$ is the angle required measuring $${75}^{\circ }$$ .
Now, to bisect the angle of $${75}^{\circ }$$ , two mentioned below steps should be followed:
Step 9: Take $$A$$ & $$L$$ as centres and draw two arcs taking any radius such that both the arcs intersect each other at point $$M$$ .
Step 10: Join $$OM$$ , $$\mathrm{\angle }MOA$$ is the angle bisector of $$\mathrm{\angle }FOA$$ .

Construction tool source: https://www.mathspad.co.uk/i2/construct.php

Note: It is very important here to learn to bisect an angle. It is always important to keep in mind how to bisect an angle as angle could be plotted by using this concept. This is a very basic question. We may have asked in a question given the line segment of base of an angle or any length could be given.