Shapes and Angles: Definition, Classification and Examples

Shapes and Angles: In our daily lives, we come across all types of shapes and angles almost everywhere. For example, the angle formed by a clock’s hands, the angle formed by two intersecting roads, the angle formed by a slice of pizza, the angle made by the corner of the doors and windows, and angles made by blades of a fan and so on. The shape of the sun is different from that of a book. The notebooks are of the same shape but different sizes.

This article will discuss two-dimensional shapes, different types of angles, and the solved examples.

What are Shapes?

Open Shape: The figure that starts and ends at the different points to form a boundary by line segments or curves is called an open shape.

Closed Shape: The figure that starts and ends at the same point to form a boundary by line segments or curves is called a closed shape.

What are Polygons?

Polygon comes from the Greek words poly, which means many, and gon, which means angle. A polygon is a simple closed curve formed by three or more line segments such that

(i) no two-line segments intersect except at their endpoints.
(ii) no two line segments with a common endpoint are coincident.

A polygon, in other words, is a simple closed two-dimensional shape created by combining straight line segments. Equilateral triangles, squares, scalene triangles, rectangles, and other shapes are examples.

NOTE: A circle is a closed curve, but it is not a polygon because it excludes line segments.

Shape of a Polygon

The number of sides determines the shape of the polygon. For example, if a polygon has three sides, it is referred to as a triangle. When a polygon has four sides, it is referred to as a quadrilateral. If a polygon has five sides, it is referred to as a pentagon, and so on.

Let us have a look at the shapes given below.

Triangle: Triangle is a polygon made of \(3\) sides and consists of \(3\) edges and \(3\) vertices. Also, the total measure of its internal angles equal to \(180^{\circ}\).

Circle: Circle is a plane geometrical round shape having all points at the same distance from the centre.

Shapes With Four Sides and Four Angles

Square: The type of quadrilateral in which all the sides are equal, and each angle measures \(90^\circ \) is called a square.

Rectangle: The type of quadrilateral in which opposite sides are of equal length, and each angle is a right angle is called a rectangle.

Parallelogram: A quadrilateral is a parallelogram if both pairs of its opposite sides are parallel.

Rhombus: The type of quadrilateral having all sides equal is called a rhombus.

Trapezium: The type of quadrilateral having exactly one pair of parallel sides is called the trapezium.

Kite: A quadrilateral is called a kite if it has two equal adjacent sides but unequal opposite sides.

What are Angles?

When two rays come from the same starting point, they make an angle. The arms of an angle are the rays that make up the angle, while the vertex of an angle is the initial point.

The symbol that represents the angle is \(\angle\). Here in the diagram, the angle formed is represented as \(\angle P Q R\).

Use of Angles

Angles play a significant role in our daily lives, as evidenced by the simplest items we use in our homes, such as tables and chairs, which are created by carpenters who employ angles to achieve the correct sizes and structure. 

When we talk about the most basic need of our lives, shelter—the buildings constructed by Architects and Engineers, angles are used to make suitable designs of buildings, houses, roads, and other structures. Athletes employ angles to improve their performance in activities such as steering a car, throwing a baseball, shooting a basketball, kicking a soccer ball, and so on.

Types of Angles

There are various sorts of angles, which are listed below:

1. Zero angle
2. Acute angle
3. Obtuse angle
4. Right angle
5. Straight angle
6. Reflex angle
7. Complete/Full angle

Zero Angles: \(P Q\) is a ray. The starting point of the given ray is on the left side, and also it is parallel to the surface of the earth. Hence, the ray \(P Q\) represents the zero angle.

Let us look at an example of zero angles.

The hands of a clock create a zero angle at \(12\) o’clock. Look at the image below.

Acute Angle: An angle that lies between \(0^{\circ}\) to \(90^{\circ}\) is known as an acute angle.

Let us look at an example of an acute angle. The hands of a clock create an acute angle at \(2\) o’clock. Look at the image below.

Obtuse Angle: An angle that is greater than \(90^{\circ}\) but less than \(180^{\circ}\) is known as an obtuse angle.

Let us look at an example of an obtuse angle. The hands of a clock create an obtuse angle at \(5\) o’clock. Look at the image below.

Right Angle: An angle that is precisely \(90^{\circ}\) is known as a right angle.

Let us look at an example of a right angle. The hands of a clock create a right angle at \(3\) o’clock. Look at the image below.

Straight Angle: When the arms of the angles lie in the opposite direction, they form a straight angle. That is, an angle which is of \(180^{\circ}\) is known as a straight angle.

Let us look at an example of a straight angle.

The hands of a clock create a straight angle at \(6\) o’clock. Look at the image below.

Reflex Angle: An angle that is greater than \(180^{\circ}\) but less than \(360^{\circ}\) is known as a reflex angle.

In the below diagram, the shown angle is represented as reflex \(\angle P Q R\).

Let us look at an example of a reflex angle.

The hands of a clock create a reflex angle at \(12:35\,{\text{PM}}\) when observed in a clockwise direction. Look at the image below.

Complete/full angles: An angle of \(360^{\circ}\) is known as a complete or full angle. It is equivalent to two straight angles or four right angles. A complete angle and a zero angle are represented in the same way, but there is one difference: the degree of rotation.

Let us look at an example of a complete angle.

The hands of a clock create a complete angle at \(12\) o’clock. Look at the image below.

Complementary Angles and Supplementary Angles

Complementary Angles: Two angles whose sum is \(90^{\circ}\) are known as complementary angles. Whenever two angles are said to be complementary, each of the angles is said to be the complement of the other. As shown in the diagram below, \(30^{\circ}\) angle is the complement of \(60^{\circ}\) angle or vice versa because their sum is \(90^{\circ}\).

Supplementary Angles: Two angles whose sum is \(180^{\circ}\) are known as supplementary angles. When two angles are supplementary, each angle is said to be the supplement of the other. As shown in the diagram below, \(60^{\circ}\) angle is the supplement of \(120^{\circ}\) angle or vice versa because their sum is \(180^{\circ}\).

Solved Examples – Shapes and Angles

Q.1. Write the number of sides of the polygons given below and name them:

Ans: (i) In the given figure, the number of sides of the polygon is five, so we call it a pentagon.
(ii) In the given figure, the number of sides of the polygon is eight, so we call it an octagon.
(iii) In the given figure, the number of sides of the polygon is six, so we call it a hexagon.
(iv) In the given figure, the number of sides of the polygon is three, so we call it a triangle or a trigon.

Q.2. Classify the following angles as acute, obtuse, right, and straight angles.
a) \(125^{\circ}\)
b) \(30^{\circ}\)
c) \(90^{\circ}\)
d) \(180^{\circ}\)
Ans: a) \(125^{\circ}\) – Obtuse angle
b) \(30^{\circ}\)- Acute angle
c) \(90^{\circ}-\) Right angle
d) \(180^{\circ}-\) Straight angle

Q.3. Write the number of acute and obtuse angles in the letter \(A\).
Ans: The letter A is made up of \(3\) line segments that intersect at three points and makes \(5\) angles less than \(180\) degrees. Three of these angles are acute, and two are obtuse.

Q.4. How many sides and vertices, a quadrilateral has?
Ans: A quadrilateral has \(4\) sides and \(4\) vertices.

Q.5. Find the supplementary of the angle \(130^{\circ}\).
Ans: We know that two angles are supplementary when they add up to \(180^{\circ}\).
Let the supplementary angle be \(x\).
Now, \(x+130^{\circ}=180^{\circ}\)
\(x=180^{\circ}-130^{\circ}=50^{\circ}\)
Hence, the supplementary angle is \(50^{\circ}\).

Summary

We learned about open and closed curves, polygons and their types, two-dimensional shapes, shapes with four sides and four angles, angles and their types, supplementary and complementary angles, and solved problems in this article.

Learn About Different Geometrical Shapes

FAQs

Q.1. What are shapes?
Ans: A shape is defined as an object’s boundaries or outline. It is the surface that we see, and it is independent of the object’s size or colour.

Q.2. What are angles?
Ans: An angle is defined as the figure created by two rays meeting at a common endpoint in geometry.

Q.3. What are quadrilaterals?
Ans: Quadrilaterals are polygons with four sides and four angles.

Q.4. What are the different classifications of a polygon?
Ans: Based on the number of sides, polygons are classified as:

Q.5. What shape has \(2\) parallel sides and \(2\) right angles?
Ans:  A right trapezoid has \(2\) parallel sides and \(2\) right angles.

We hope this detailed article on shapes and angles proves helpful. Feel to ask your doubts or queries in the comment section below. We will surely get back to you at the earliest. Embibe wishes you all the best for your preparations!