The sum of interior angles of a quadrilateral is
The Correct Answer and Explanation is :
The sum of the interior angles of any quadrilateral is always 360 degrees.
Explanation:
To understand this, let’s break down the reasoning:
A quadrilateral is a polygon with four sides. The sum of the interior angles of any polygon can be calculated using the formula:
[
\text{Sum of interior angles} = (n – 2) \times 180^\circ
]
Where (n) is the number of sides of the polygon.
For a quadrilateral, (n = 4), so the formula becomes:
[
\text{Sum of interior angles} = (4 – 2) \times 180^\circ = 2 \times 180^\circ = 360^\circ
]
This means that the sum of the interior angles in any quadrilateral (whether it’s a square, rectangle, trapezoid, rhombus, or any other type) is always 360 degrees.
Why does this work?
This formula works because it’s based on the idea of dividing the polygon into triangles. Every polygon can be divided into triangles, and the sum of the interior angles of any triangle is always 180 degrees.
For example, a quadrilateral can be divided into two triangles. Each triangle has 180 degrees, so the sum of the interior angles of the quadrilateral is:
[
180^\circ + 180^\circ = 360^\circ
]
Visualizing the Concept:
If you draw a quadrilateral and connect two opposite corners to form two triangles, you’ll notice that the angles of these triangles add up to 360 degrees. This helps reinforce the fact that the sum of the angles in a quadrilateral is always 360 degrees, regardless of the specific type of quadrilateral.
Now, I’ll generate an image that shows the division of a quadrilateral into two triangles to visualize this idea.
Here is the illustration that shows how a quadrilateral can be divided into two triangles, reinforcing the idea that the sum of the interior angles is 360 degrees. The diagram clearly demonstrates the relationship between the angles of the quadrilateral and how they add up. Let me know if you need further explanations or details!
