Question

the sum of the interior angles of a quadrilateral is ______.
180°
90°
360°
270°

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

The formula for the sum of interior angles of a polygon with \( n \) sides is \( S=(n - 2)\times180^{\circ} \).

Step2: Identify the number of sides of a quadrilateral

A quadrilateral has \( n = 4 \) sides.

Step3: Substitute \( n = 4 \) into the formula

Substitute \( n = 4 \) into \( S=(n - 2)\times180^{\circ} \), we get \( S=(4 - 2)\times180^{\circ}=2\times180^{\circ} = 360^{\circ} \).

Answer:

\( 360^{\circ} \) (the option corresponding to \( 360^{\circ} \))