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.

You are watching: How many degrees is in a quadrilateral

In this article, you will certainly learn:

What a square is.How the different types of quadrilaterals watch like.The properties of quadrilaterals.


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.


 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

All sides space congruent by definition.The diagonals bisect the angles.The diagonals in a kite bisect each other at appropriate angles.


Properties of Quadrilaterals

The properties of quadrilateral include:

Every quadrilateral has 4 sides, 4 vertices, and also 4 angles.4The total measure of all the 4 interior angle of a square is always equal to 360 degrees.The sum of inner angles of a square fits the formula that polygon i.e.

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:

Convex quadrilaterals: These room the quadrilaterals with internal angles much less than 180 degrees, and the two diagonals space inside the quadrilaterals. They include trapezium, parallelogram, rhombus, rectangle, square, kite, etc.Concave quadrilaterals: These are the quadrilaterals v at the very least one interior angle greater than 180 degrees, and at least one that the two diagonals is external the quadrilaterals. A dart is a concave quadrilateral.

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.


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

⇒ x° + 80° + 2x° + 70° =360°


⇒ 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.


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


⇒ 70x + 80 = 360

Subtract both political parties by 80 come get;

⇒ 70x = 280

Divide both sides by 70.

See more: How To Fix " The Instruction At 0X0000 Referenced Memory At 0X00000

⇒ 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.