Different forms of forms differ from each other in terms of sides or angles. Many shapes have 4 sides, however the distinction in angles on their sides makes them unique. We speak to these 4-sided forms the quadrilaterals.

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**In this write-up, you will learn:**

## What is a Quadrilateral?

As the word argues, ‘**Quad**’ suggests four and ‘**lateral**’ means side. Because of this a quadrilateral is a **closed two-dimensional polygon made up of 4-line segments**. In basic words, **a quadrilateral is a shape via four sides**.

Quadrilaterals are everywhere! From the books, chart records, computer system keys, tv, and mobile screens. The list of real-human being examples of quadrilaterals is endmuch less.

## Types of Quadrilaterals

There are **6 quadrilaterals in geometry**. Some of the quadrilaterals are sucount familiar to you, while others might not be so familiar.

Let’s take a look.

RectangleSquaresTrapeziumParallelogramRhombusKite** A rectangle **

A rectangle is a quadrilateral through 4 appropriate angles (90°). In a rectangle, both the pairs of oppowebsite sides are parallel and equal in length.

**Properties of a rhombus**

## Properties of Quadrilaterals

*The properties of quadrilaterals include:*

Sum of inner angles = 180 ° * (n – 2), wbelow n is equal to the variety of sides of the polygon

Rectangles, rhombus, and also squares are all types of parallelograms.A square is both a rhombus and also a rectangle.The rectangle and rhombus are not square.A parallelogram is a trapezium.A trapezium is not a parallelogram.Kite is not a parallelogram.### Classification of quadrilaterals

*The quadrilaterals are classified into two basic types:*

Tbelow is one more less widespread form of quadrilaterals, referred to as complicated quadrilaterals. These are crossed figures. For example, crossed trapezoid, crossed rectangle, crossed square, etc.

Let’s job-related on a few example problems about quadrilaterals.

*Example 1*

The inner angles of an ircontinual quadrilateral are; x°, 80°, 2x°, and 70°. Calculate the worth of x.

Solution

By a residential or commercial property of quadrilaterals (Sum of internal angles = 360°), we have actually,

⇒ x° + 80° + 2x° + 70° =360°

Simplify.

⇒ 3x + 150° = 360°

Subtract 150° on both sides.

⇒ 3x + 150° – 150° = 360° – 150°

⇒ 3x = 210°

Divide both sides by 3 to get;

⇒ x = 70°

Thus, the worth of x is 70°

And the angles of the quadrilaterals are; 70°, 80°, 140°, and 70°.

*Example 2*

The internal angles of a quadrilateral are; 82°, (25x – 2) °, (20x – 1) ° and (25x + 1) °. Find the angles of the quadrilateral.

Solution

The total amount of inner angles of in a quadrilateral = 360°

⇒ 82° + (25x – 2) ° + (20x – 1) ° + (25x + 1) ° = 360°

⇒ 82 + 25x – 2 + 20x – 1 + 25x + 1 = 360

Simplify.

⇒ 70x + 80 = 360

Subtract both sides by 80 to get;

⇒ 70x = 280

Divide both sides by 70.

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⇒ x = 4

By substitution,

⇒ (25x – 2) = 98°

⇒ (20x – 1) = 79°

⇒ (25x + 1) = 101°

Therefore, the angles of the quadrilateral are; 82°, 98°, 79°, and also 101°.

*Practice Questions*

Consider a parallelogram PQRS, whereFind the 4 interior angles of the rhombus whose sides and one of the diagonals are of equal size. *Practice Questions*

Answers