Constructing 90 Degree Angle

In geometry, learning how to make a 90°, also called a right angle, is fundamental. Not only is it helpful in the construction of other angles like that of 60°, 45°, 120°, 30°, etc., but it also has lots of practical applications in real life, among which are distance measurements between planets and construction of buildings and other infrastructures. Although 90° can be quickly drawn with a protractor, this is an essential skill for students to accurately construct 90° with a compass and ruler.

In this article, we will learn to draw an angle of 90 degrees with a compass and ruler step by step.

A right angle, often referred to as a 90° angle, is an angle formed by the meeting of line segments that are perpendicular to each other. In other words, they meet in such a way that, in the end, they enclose the corners of a square.

Properties of Right Angle

• Measures Exactly 90 Degrees: A right angle always measures exactly 90 degrees. It’s one-fourth of a full circle.
• Forms a Perfect “L” Shape: When two lines meet to form a right angle, they make a perfect “L” shape.
• Found in Squares and Rectangles: All four angles in squares and rectangles are right angles. This helps give these shapes their straight, even sides.
• Indicated by a Small Square: In drawings or diagrams, a right angle is often shown with a small square at the corner to indicate it is 90 degrees.
• Basis for Perpendicular Lines: If two lines meet and form a right angle, they are called perpendicular lines. This means they cross each other to create a 90-degree angle.

Now that we’ve learned what a 90° is, let’s see how to construct a 90° angle using a compass and ruler:

Materials Required

Basic materials needed to build a 90 degree angle are:

• Compass: The compass is quite an essential instrument to use when making a 90-degree angle, as it allows one to measure and draw the arcs quite correctly.
• Ruler: A ruler will be used to take a proper reading and draw an appropriate measure of length.
• Pencil: A pencil is used to mark points, describe lines, and write comments on the paper.
• Clean Sheet of Paper: All the lines or angles are drawn on a plane and smooth surface. It also helps in seeing the drawing of the lines and angles drawn clearly to ease the construction of these.

Step-by-Step Guide

Here is the instruction to construct a 90° angle:

Step 1: Draw a straight line segment AB on the sheet.

Step 2: Place the tip of the compass at A and draw an semi-circle that intersects the line AB and name it C.

Step 3: Put the point of the drafting compass at C and draw an arc on the previously drawn arc, name that point D.

Step 4: Without changing the separation of the legs of the drafting compass, draw another arc on the first drawn semi circle and name it E.

Step 5: Keeping the same compass width, place the compass needle on the points D and E and draw an arc from each point that intersects at a point, name it F.

Step 6: Draw a straight line joining A and the point of intersection of the small arcs i.e. F. We have a 90° angle.

Tips and Tricks while Contructing 90 Degree Angle

Here are some tips and tricks to increase the accuracy of construction:

• Use a pencil and ruler to draw the line with precision and care. Measure the line well, and draw a straight line.

• While adjusting the width of the compass, make sure that it is more than half the length of AB. And while drawing the arc, ensure that the width of the compass remains unchanged.

• In drawing the required arcs, the compass should be held tightly enough so it does not waver or slip so measurements are accurate.

• Make sure your pencil is sharp so that you will get clear markings and lines; dull pencils may result in fuzz or an unclear intersection.

• Link the points of intersection and draw a straight line with the use of a ruler through the points of intersection. Ensure that the line drawn is a bit longer than the point of intersection at both extremes so that it gives a clear, sharp, and perpendicular line.

• Corners of a Square or Rectangle: When you look at the corners of a square or a rectangle, each corner makes a 90-degree angle.

• Books on a Shelf: When books are neatly placed upright on a shelf, the spine of the book forms a 90-degree angle with the shelf surface.

• Classroom Board and Floor: The board in a classroom is usually placed upright, forming a 90-degree angle with the floor.

• Window Frames: The corners of most window frames form 90-degree angles, just like the corners of a square or rectangle.

• Street Intersections: Many streets intersect at right angles, forming 90-degree angles at the corners where they meet.

In conclusion, correctly creating an angle of 90° with the help of a compass and a ruler is a strong and necessary base in geometry. Not only does it help construct angles of expected need, but it is also used in everyday life. With the aid of this step-by-step manual and regular practice, a student can apply the knowledge of the principles of geometry in confident ways in different academic and practical situations, which goes a long way in strengthening the understanding of geometry and its applicability.

Also Read,

• 60 degree Angle
• 180 degree Angle
• Complete Angle

How many 90-degree angles are in one complete turn?

There are 360 degrees in a full rotation. An angle measuring 90 degrees represents one-fourth of a full rotation. Now, 360/90 = 4. Therefore, there are four angles of 90 degrees each in the whole rotation..

Examples of 90 degrees in real life.

1. Corners of Room: The angles where the floor or ceiling meets the walls are generally right angles of 90°.
2. Books: The closed book has edges that are 90-degree angles.
3. Television and Computer Screens: The edges of most screens form right angles.
4. Crossroads: A few street junctions mark 90°.

How does a 90-degree angle look like?

A 90-degree angle, or a right angle, is therefore shaped like the corner of a square or rectangle. It is where two lines meet to form an L shape, creating a perfect quarter of a circle. It can be shown by a small square at the corner where two lines meet.

What are the 7 Different Types of Angle?

1. Acute Angle: An angle that measures less than 90 degrees.
2. Right Angle: An angle exactly 90 degrees.
3. Obtuse Angle: An angle between 90 and 180 degrees end .
4. Straight angle: An angle which measures exactly 180 degrees.
5. Reflex Angle: An angle between 180° and 360° in size.
6. Full Turn: An angle measuring 360 degrees.
7. Adjacent Angles: Two angles that share a common side and a common vertex but do not overlap

How to Measure 90 Degrees with Protractors?

To Measure 90 Degree Angles with Protractors – Put the center of the protractor on the vertex of the angle. Line up one of the angle’s sides with the 0 line on the protractor. Look to see where the other side of the angle crosses the number 90 on the protractor.