### Mathematics Class IX

Number Systems
Polynomials
Coordinate Geometry
Lines and Angles
Triangles
Circles
Constructions
Heron’s Formula
Surface Areas and Volumes
Statistics
Probability

# Angle Sum Property of a Quadrilateral

The sum of the four angles of a quadrilateral is 360°

If we draw a diagonal in the quadrilateral, it divides it into two triangles.

And we know the angle sum property of a triangle i.e. the sum of all the three angles of a triangle is 180°.

The sum of angles of .

The sum of angles of .

By adding both we get Hence, the sum of the four angles of a quadrilateral is 360°.

Example

Find A and D, if BC || AD and B = 52° and C = 60° in the quadrilateral ABCD.

Solution:

Given BC ∥ AD, so ∠A and ∠B are consecutive interior angles.

So A + B = 180° (Sum of consecutive interior angles is 180°). B = 52° A = 180°- 52° = 128° A + B + C + D = 360° (Sum of the four angles of a quadrilateral is 360°). C = 60°

128° + 52° + 60° + D = 360° D = 120° A = 128° and D = 120°.

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