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What is the sum of angles in a quadrilateral?
180 degrees
270 degrees
360 degrees
540 degrees
360 degrees
Remember that any polygon can be divided into (n−2) triangles by drawing diagonals from a single vertex, where n is the number of sides.
A quadrilateral with 4 sides and 4 interior angles.
S=(n−2)×180°
Remember that any polygon can be divided into (n−2) triangles by drawing diagonals from a single vertex, where n is the number of sides.
Confusing the sum of interior angles of a quadrilateral (360°) with that of a triangle (180°).
Identify Polygon Formula
The sum of interior angles for any n-sided polygon is given by the formula S=(n−2)×180°.
S=(n−2)×180°
Identify Number of Sides
A quadrilateral has n=4 sides and 4 vertices.
n=4
Calculate the Angle Sum
Substitute n=4 into the formula: S=(4−2)×180°=2×180°=360°.
S=(4−2)×180°=360°
C is correct because the sum of interior angles of a quadrilateral is 360°.
This formula applies universally to any polygon with n sides, allowing you to easily find the angle sum for pentagons, hexagons, and beyond.
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