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Question

The sum of all angles of a quadrilateral is
(a) 180
(b) 270
(c) 360
(d) 480


Solution

Let ABCD is a Quadrilateral.

A,B,C and D are the angles of Quadrilateral.

BD is a diagonal.


In figure,

Diagonal BD divides the quadrilateral into two triangles.

Sum of the angle of quadrilateral ABCD= Sum of the angles of ADC+ Sum of the angles of BDC

A+B+C+D

=(x+y+u)+(z+w+v)

=180+180 [Since, Sum of the angles of a triangle is 180]

=360

A+B+C+D=360

Therefore, the sum of all angles of a quadrilateral is 360.

Hence, Option C is correct.


Mathematics
RS Aggarwal (2017)
Standard VII

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