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 foursided polygon. To find the sum of its angles, we can use the formula for the sum of angles in an nsided polygon, which is (n2) times 180 degrees. Here, n = 4.
Answer
The sum of the interior angles in a quadrilateral is \( 360^\circ \).
Answer for screen readers
The sum of the interior angles in a quadrilateral is ( 360^\circ ).
Steps to Solve

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

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: $$ \text{Sum of angles} = (n  2) \times 180^\circ $$

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

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 ).
More Information
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 doublecheck your calculations.