Question

Prove that the sum of the angles of a
quadrilateral is 360°​

Answer 1

there are a quadrilateral named ABCD.

if we drawn BD

then we get two triangles named ABD and BCD.

we know that the sum of the angles of a triangle is 180 degree....

so sum of angles of two triangles are 180+180=360 degree...

I think this will help you....

Answer 2

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°.