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.
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
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Identify the number of sides A quadrilateral has 4 sides, so we have ( n = 4 ).
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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: $$ \text{Sum of angles} = (n - 2) \times 180^\circ $$
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Plug in the value of n Substituting ( n = 4 ) into the formula, we get: $$ \text{Sum of angles} = (4 - 2) \times 180^\circ $$
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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 double-check your calculations.
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