# What is the sum of the angles of a quadrilateral?

#### Understand the Problem

The question is asking for the sum of the interior angles in a quadrilateral. A quadrilateral is a four-sided polygon. To find the sum of its angles, we can use the formula for the sum of angles in an n-sided polygon, which is (n-2) times 180 degrees. Here, n = 4.

The sum of the interior angles in a quadrilateral is $$360^\circ$$.

The sum of the interior angles in a quadrilateral is ( 360^\circ ).

#### Steps to Solve

1. Identify the number of sides A quadrilateral has 4 sides, so we have ( n = 4 ).

2. Apply the formula for sum of interior angles The formula for the sum of the interior angles in an ( n )-sided polygon is given by: $$\text{Sum of angles} = (n - 2) \times 180^\circ$$

3. Plug in the value of n Substituting ( n = 4 ) into the formula, we get: $$\text{Sum of angles} = (4 - 2) \times 180^\circ$$

4. Calculate the result Now we perform the calculation: $$\text{Sum of angles} = 2 \times 180^\circ = 360^\circ$$

The sum of the interior angles in a quadrilateral is ( 360^\circ ).

In geometry, the sum of the interior angles of any quadrilateral, regardless of its shape, will always be ( 360^\circ ). This is a fundamental property that helps when analyzing more complex polygons.

#### Tips

• A common mistake is confusing the formula for the sum of angles in different types of polygons. Remember that the formula changes depending on the number of sides.
• Another mistake can be incorrectly subtracting or multiplying, so always double-check your calculations.
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