Question

prove that in a quadrilateral the sum of all angle is 360°​

Answer 1

Given- A quad. ABCD

To Prove- angle A + angle B +angle C + angle D = 360 degree

Const- join BD

proff - since the sum of the angles of a triangle is 180 degree, we have angle A + angle 1 + angle 2 =180 degree ..... (i) ( sum of angle of triangle ABD)

and angle 3 + angle C + angle 4 = 180 degree ....(ii)( sum of angle of triangle BCD).

on adding (i) and (ii), we get angle A + angle C + ( angle 1 + angle 3 ) + (angle 2 + angle 4) = 360 degree

angle A + angle C + angle B + angle D = 360 degree { angle 1 + angle 3 = angle B and angle 2 + angle 4 = angle A }

angle A + angle B + angle C + angle D = 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°.