Right Angle: Definition, Properties, and Examples

A right angle is defined as a 90-degree angle. It can be found in the corners of a room, the edges of boxes, the screen of a phone, and other places.

She observed the angle made by clock hands at 3:00 pm, 3:00 pm, one-fourth piece of a pizza, the corners of a room; Priya noticed that right angles are all around us. Do you feel the same? This section will explore the whole new world of the right angles. The topic will be as clear as a crystal by discovering interesting facts about right-angle.

What is an Angle?

An angle is formed when two rays originate from the same point. The rays making an angle are called the arms of an angle, and the originating point is called the vertex of an angle.

Chairs, windows, books, two intersecting roads, hands of a clock, blades of a fan, corners of a room, etc.—these are some of the things that we see in our everyday lives. When observed closely, they form angles. There are many types of angles between the edges of plane surfaces.

Angle is represented by the symbol \(\angle .\) In the above-given figure, the angle formed is represented as \(\angle PQR.\)

Types of Angles

The different types of angles are mentioned below:
1. Zero angle
2. Acute angle
3. Obtuse angle
4. Right angle
5. Straight angle
6. Reflex angle
7. Complete/Full angle

Zero Angle

An angle that is equal to \({0^ \circ }\) is called a zero angle. In the diagram below, \(PQ\) and \(PR\) are two rays originating from the same point and are in the same direction. Hence, they represent zero angles.

Acute Angle

An angle whose measure is more than \({0^ \circ }\) but less than \({90^ \circ }\) is known as an acute angle.

Obtuse Angle

An angle whose measure is more than \({90^ \circ }\) but less than \({180^ \circ }\) is known as an obtuse angle.

Right Angle

An angle whose measure is equal to \({90^ \circ }\) is known as a right angle.

Straight Angle

When the arms of the angles lie in the opposite direction, they form a straight angle. That is, an angle whose measure is \({180^ \circ }\) is known as a straight angle or flat angle. One straight angle is the combination of two right angles.

Reflex Angle

An angle whose measure is more than \({180^ \circ }\) but less than \({360^ \circ }\) is known as a reflex angle.

Complete Angle

An angle which is of \({360^ \circ }\) is known as a complete or full angle. It is equivalent to two straight angles or four right angles.

What is a Right Angle?

A right angle is an internal angle that is equal to \({90^ \circ }\)

Can you see that special symbol like a box in the corner? That box itself says it is a right angle. It simply means that if anytime you encounter the box in the corner, it means, the angle is a right angle.

All the angles shown above are right angles. If we speak plainly, a right angle can be in any orientation or rotation if the internal angle is \({90^ \circ }\)

Right angles play an important role in areas of mathematics such as geometry and trigonometry. When two straight lines intersect each other at \({90^ \circ }\) or fall perpendicularly to each other at the point of intersection, they form a right angle. 

And mind it!!!!

“Never argue with a \({90^ \circ }\) because it’s always RIGHT.”

Shape of a Right Angle

A vertical and a horizontal line make the most common right angles. With the help of a compass, follow the steps to construct a right angle:

1. Draw a ray \(OA\)
2. Taking \(O\) as a centre and taking any radius, draw an arc cutting \(OA\) at \(B\)

3. Now, taking \(B\) as a centre, and with the same radius before, draw an arc intersecting the previously drawn arc at point \(C\)
4. With \(C\) as the centre and the same radius, draw an arc cutting at \(D\).

5. With \(C\) and \(D\) as centres and radius more than \(\frac{1}{2}CD,\) draw two arcs intersecting at \(P.\)
6. Join \(OP\).

\(\angle AOP\, = \,90\) degrees. And, thus, the above-given figure obtained is what we call a right angle.

Right Angle Calculator

Some devices are used for measuring the right angle. The name of the devices is as follows.

1. Protractor: A protractor is a flat, semi-circular piece of plastic or metal used to measure angles.

2. Set Square: A set square is a flat triangular piece of plastic or other material, having corners of precise angles, used in technical drawings.

3. Try Square: A try square is a woodworking tool used for marking and checking \(90 – \)-degree angles on a piece of wood.

Applications of a Right Angle

1. A right angle is mainly used in trigonometry. We can use right triangles to find distances if you know an angle of elevation or an angle of depression. 

2. A right angle is used in a right-angle triangle.

3. A right-angled triangle is the one with three sides, “base”, “hypotenuse”, and “perpendicular”, with the angle between the base and the perpendicular is \({90^ \circ }\)

Right Angle Triangle Properties

Some of the important properties of a right triangle are listed below.
1. A right triangle has only one angle equal to \({90^ \circ }\).
2. The angles other than the right angle must be less than \({90^ \circ }\).
3. The side opposite to the vertex of \({90^ \circ }\) is called the hypotenuse.
4. The other two sides adjacent to the right angle are called base and perpendicular.

Right Angle Isosceles Triangle

When the two sides other than the hypotenuse, that is, base and perpendicular, are equal in a right triangle, it is called a right-angle isosceles triangle. In this type of triangle, the angles made by the base and perpendicular with the hypotenuse are equal.

Solved Examples

Q.1. Priya wants to know which types of angles are greater than the right angle. Can you name the angles that are greater than the right angle?
Ans: Any angle whose measure is greater than \(90\) degrees is greater than a right angle. Such angles are obtuse angle, straight angle, reflex angle, and complete angle.

Q.2. Can you name the angle made between the hour hand and minute hand of a clock given below
Ans: We can see that the hour hand is at \(3\) and the minute hand is at \(12\) So, the two hands of the clock are making an angle of \(90\) degrees.

Q.3. Are all the triangles with one right angle are called right-angled triangles?
Ans: Yes, all the triangles with one right angle are called a right-angled triangle.

Q.4. Give some examples of a right angle?
Ans: Many real-life examples contain right angles such as corners of books, tables, crossroads, boards in classrooms, badminton or volleyball courts, doors, and windows of a house, which have their corners in the shape of a right angle.

Q.5. Can a triangle have two right angles?
Ans: No, a triangle can never have two right angles. We know that the sum of three angles of a triangle is\({180^ \circ.}\) So, if a triangle has two right angles then the measure of the third angle has to be \({0^ \circ }\), which means the third side will overlap with the other side. Hence, it is not possible to have a triangle with two right angles.

Summary

In this article, we learned the definition of an angle. We learned about a right angle. Along with that, we learned the definition of other angles as well. We also learned how to draw a right angle and the instruments used to measure the right angle. Finally, we also learned the application of right angles and right-angled triangles in real life.

FAQs

Q.1. What are the \(16\) basic shapes in geometry?
Ans: The \(16\) basic shapes in geometry are circle, square, rectangle, parallelogram, trapezium, rhombus, quadrilateral, kite, equilateral triangle, isosceles triangle, scalene triangle, pentagon, hexagon, trapezoid, cube, cuboid, sphere, pyramid.

Q.2. What do you mean by a right angle?
Ans: In geometry and trigonometry, a right angle is formed when two straight lines intersect each other at \(90\) degrees or are perpendicular to each other at the point of intersection.

Q.3. Is a right angle equal to \(90\) degrees?
Ans: Yes, a right angle is always \(90\) degrees.

Q.4. How do you measure a \(90\) degree angle?
Ans: We measure a \(90\)-degree angle with the help of a compass, set square and try square.

Q.5. What are the angles of a right triangle?
Ans: In a right triangle, since the sum of all the interior angles of any triangle must be \(180\) degrees, the three angles include one right angle and two acute angles whose sum is equal to \(180\) degrees. Hence, a right triangle has two acute angles other than the right angle.

We hope this article on right angles has provided significant value to your knowledge. If you have any queries or suggestions, feel to write them down in the comment section below. We will love to hear from you. Embibe wishes you all the best of luck!