CONSTRUCTION OF ANGLES

In Euclidian Geometry, an angle is a shape formed by two rays which are also known as arms at their common point known as a vertex. We draw angles with the help of a protractor, but we can also construct angles without using protractors but with a compass and ruler.

Types of Angles-

Acute Angle: The angle which lies between 0 and 90 degrees is known as an acute angle.

For example, 45 degrees, 37 degrees, etc.

Right Angle: The angle which measures 90 degrees is known as the right angle.

Obtuse Angle: The angle which is greater than 90 degrees but less than 180 degrees is known as an obtuse angle.

For example, 91 degrees, 107 degrees, etc.

Straight Angle: The angle which is equal to 180 degrees is known as the straight angle.

Reflex Angle: The angle which lies between 180 degrees and 360 degrees is known as a reflex angle.

For example, 270 degrees, 189 degrees, etc.

Complete angle or Full Rotation: The angle is equal to 360 degrees. It corresponds to the central angle of the complete circle.

Construction of angles using Protractor-

You can construct an angle using a protractor with the help of the following steps:

1. Draw a line segment namely OB.
2. At one end of the line segment, place the centre point of the protractor. Note that line segment AB should be aligned with the line of a protractor.
3. Mark point A, at the angle you required.
4. Join point A with O, You have constructed the angle AOB.

Construction of angles using Ruler and compass-

You have to follow the following steps to construct an error-free Angle:-

1. Draw a ray of random length namely OB.
2. By taking any of the endpoints let’s say O as a centre and any width as the radius of the semicircular arc, draw it so that it should touch the line segment OB and mark it as R.
3. Without changing the radius, With R as a centre, create another arc, this point will be named P.
4. Repeat the above process that is in point 3rd, and draw a new point Q.
5. Draw two other arcs taking centre as points Q and P. such that these two arcs are intersecting each other at a new point A.
6. Join the points A and O, you will get the perpendicular line, which is making a 90 degrees angle with line segment OA.
7. Then, using the same radius to draw an arc in step 2 draw two arcs with R and P as centres. Mark the point of intersection of these arcs as V. Now join the points O and V . You will get an angle of 45 degrees.

Construction of a 60-degree angle using a ruler and compass-

60 degrees is one of the most basic constructions, it will make it easier for constructing angles of several other measures. The steps are:

1. Draw a line segment OB.
2. Take the compass and set it up to a convenient radius. Place its pointer at O and make an arc that meets the line OB at say, Q.
3. Now, Place the compass pointer at P and mark an arc that should pass through O and also intersect the previous arc at a point, say A.
4. Now, join point A and O using the line segment.
5. You have constructed a 60 degree angle.

Construction of a 22 and a half degree angle using a ruler and compass-

We have constructed a 90 degree and 45-degree angle above, so If I bisect a 45-degree angle, we can easily get a 22 and half-degree angle, that’s the thing that we will do here.

1. Draw a line segment OA.
2. With O as a centre with any radius, draw an arc that cuts the line segment OA at point P.
3. Now, take P as a centre, draw another arc that cuts the previous arc at point B.
4. Take B as a centre, draw another arc that cuts the arc at point C.
5. Now, take B and C as centres, draw two arcs simultaneously, say these arcs are intersecting on point Z.
6. Join O and Z the angle will form 90 degrees.
7. Let, the arc PC cuts the Perpendicular line at E.
8. Now, draw two arcs simultaneously from points E and P which intersect at point N. The angle will form 45 degrees.
9. Let, the arc EP cuts the line of a 45-degree angle at T. 
10. Now, draw another two arcs from point T and P, which intersects at point F.
11. The angle FOA will form is 22 and a half degrees angle.
12. Hence, we have constructed it.

Conclusion-

Here, we have studied the construction of angles which is an important aspect of construction in geometry. We have studied two methods for construction, i. Using Protractor ii. Using Compass. Above we have described in detail as well as step-by-step methods to construct various degrees of angles. We have discussed different types of angles like acute angle, obtuse angle, reflex angle, obtuse angle, straight angle. We have talked about the construction of 60 degrees angles using, a ruler and compass, the construction of 2212 degree angles using a ruler and compass. It is easy to construct such angles by using the above-listed steps.