Different varieties of shapes differ from each other in terms of sides or angles. Many shapes have actually 4 sides, yet the distinction in angles on your sides renders them unique. We speak to these 4-sided forms the quadrilaterals.

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**In this article, you will certainly learn:**

## What is a Quadrilateral?

As the word suggests, ‘**Quad**’ means four and ‘**lateral**’ way side. As such a quadrilateral is a **closed two-dimensional polygon consisted of of 4-line segments**. In simple words, **a quadrilateral is a shape with four sides**.

Quadrilaterals room everywhere! from the books, chart papers, computer keys, television, and also mobile screens. The list of real-world instances of quadrilateral is endless.

## Types the Quadrilaterals

There are **six quadrilateral in geometry**. Some of the quadrilaterals space surely acquainted to you, while others might not it is in so familiar.

Let’s take it a look.

RectangleSquaresTrapeziumParallelogramRhombusKite** A rectangle **

A rectangle is a quadrilateral through 4 right angles (90°). In a rectangle, both the bag of the contrary sides room parallel and also equal in length.

**Properties the a rhombus**

## Properties of Quadrilaterals

*The properties of quadrilateral include:*

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

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

*The quadrilaterals space classified into two basic types:*

There is another less common form of quadrilaterals, called complicated quadrilaterals. These are crossed figures. For example, overcome trapezoid, overcome rectangle, overcome square, etc.

Let’s occupational on a few example problems around quadrilaterals.

*Example 1*

The inner angles of an irregular quadrilateral are; x°, 80°, 2x°, and also 70°. Calculation the value of x.

Solution

By a residential property of quadrilateral (Sum of interior angles = 360°), we have,

⇒ x° + 80° + 2x° + 70° =360°

Simplify.

⇒ 3x + 150° = 360°

Subtract 150° on both sides.

⇒ 3x + 150° – 150° = 360° – 150°

⇒ 3x = 210°

Divide both political parties by 3 come get;

⇒ x = 70°

Therefore, the value of x is 70°

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

*Example 2*

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

Solution

The full sum of internal angles the 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 political parties by 80 come 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 square are; 82°, 98°, 79°, and 101°.

*Practice Questions*

Consider a parallel PQRS, whereFind the 4 interior angles the the rhombus who sides and also one that the diagonals are of equal length. *Practice Questions*

Answers