
Shortcut Trick
The sum of the interior angles of any polygon with n sides is given by the formula: (n − 2) × 180°.
For a quadrilateral, the number of sides is n = 4.
Substituting n = 4 into the formula:
Sum of interior angles = (4 − 2) × 180° = 2 × 180° = 360°.
∴ The correct answer is 360°.

Alternate Method
Given:
A polygon is a quadrilateral (number of sides, n = 4).
Formula Used:
Any quadrilateral can be divided into two triangles by drawing a single diagonal.
The sum of the interior angles of a triangle is always 180°.

Calculations:
Let ABCD be a quadrilateral. Draw diagonal AC, which divides the quadrilateral into two triangles: ΔADC and ΔABC.
⇒ Sum of angles in ΔADC = ∠D + ∠DAC + ∠DCA = 180°
⇒ Sum of angles in ΔABC = ∠B + ∠BAC + ∠BCA = 180°
⇒ Total sum of interior angles of quadrilateral ABCD = Sum of angles in ΔADC + Sum of angles in ΔABC
⇒ Total sum = 180° + 180°
⇒ Total sum = 360°
Let us analyze why the other options are incorrect:
⇒ Option (1) 180° is incorrect because 180° is the sum of the interior angles of a triangle (3-sided polygon).
⇒ Option (2) 270° is incorrect because there is no standard convex polygon whose interior angle sum is 270°.
⇒ Option (3) 390° is incorrect because the sum of interior angles of any polygon must be a multiple of 180°.
∴ The correct answer is 360°.

Additional Information
Sum of Exterior Angles
For any convex polygon, regardless of the number of sides, the sum of the exterior angles is always 360°.
Interior Angle of a Regular Polygon
Each interior angle of a regular polygon with n sides is given by the formula: [(n − 2) × 180°] ÷ n.
Types of Quadrilaterals
Common quadrilaterals include squares, rectangles, parallelograms, trapezoids, rhombuses, and kites, all of which have interior angles summing to exactly 360°.