Question

Prove that sum of all angles of quadrilateral is 360

Answer 1

by using formula
(n-2)*180
here n is number of side figure has
so
quadrilateral has 4 side
=(4-2)*180
=2*180
=360

Answer 2

Given:

• In quadrilateral ABCD

• AC is the diagonal

• It divides the quadrilateral into triangles namely ∆ABC and ∆ADC

Required To Prove:

Sum of all angles of the quadrilateral is equal to 360°

Proof:

In ∆ABC,

The angles are

• ∠BAC

• ∠BCA

• ∠CBA

∠BAC + ∠BCA +∠CBA = 180° $\to 1$

Since sum of all angles of a triangle are equal to 180°

In ∆ADC,

The angles are

• ∠DAC

• ∠DCA

• ∠CDA

∠DAC + ∠DCA +∠CDA = 180° $\to 2$

Since sum of all angles of a triangle are equal to 180°

From $1,2$

1+2= 180°+ 180°

∠BAC + ∠BCA +∠CBA + ∠DAC + ∠DCA +∠CDA = 180+180 °

∆ABC + ∆ADC = 180+180

∆ABC + ∆ADC=360°

Therefore ABCD = 360°

Therefore the sum of all angles of quadrilateral is 360°