Question

Prove the sum of all 4 angle of a quadrilateral is 360 degree

Answer 1

if consider a quadrilateral ABCD ....

divide the quadrilateral ABCD into two triangles by drawing a diagonal AC..

now....according to angle sum of triangles...

ABC = 180 & ACD = 180

but.. ABC + ACD = ABCD quadrilateral

therefore.... 180 + 180 = 360

therefore angle sum property of a quadrilateral = 360 degree

Answer 2

$\huge\sf \orange{hello}...$

Statement :

sum of the angles of quadrilateral is 360°

To Prove :

∠A + ∠B + ∠C + ∠D = 360°

Proof :

In ∆ ABC , m∠4 + m∠5+m∠6 = 180°

[ using angle a property of a triangle]

Also , in ∆ ADC , m∠1 + m∠2+m∠3= 180°

Sum of the measures of ∠A, ∠B , ∠C and ∠D of a quadrilateral

m∠4 + m∠5+ m∠6 + m∠1 + m∠2 +m∠3 = 180°+ 180°

→ ∠A + ∠B + ∠C + ∠D = 360°

Thus , sum of measure of four angles of quadrilateral is 360°.

thanks..