Question

prove that the sum of the angle of a quadrilateral is 360°

Answer 1

GIVEN-

ABCD is a quadrilateral

TO PROVE-

A+B+C+D=360

CONSTRUCTION -

Diagonal AC is drawn

PROOF -

triangles ABC&ADC are formed due to construction

we know that sum of all angles of triangle is 180

so

180+180=360

so sum of all angles of quadrilateral is 360

PROVED

Answer 2

Consider a quadrilateral ABCD.

Draw a diagonal AC.

It forms two triangles ΔABC, ΔADC.

Let the angles in the triangles are 1 , 2 , 3 , 4 , 5 , 6 .

We know that :
1 + 2 + 3 = 180 ( Angle-Sum property)
4 + 5 + 6 = 180 ( Angle sum property)

Now,

1 + 2 + 3 + 4 + 5 + 6 = A + B + C + D

2 ( 180 ) = A + B + C + D

A + B + C + D = 360° .

Hence, proved that Sum of angles in a quadrilateral = 360°