Question

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

Answer 1

Let ABCD be a quadrilateral . join ac. clearly, angle 1 + angle 2 =.......(I) and angle 3 + angle 4= .... (ii) , we know that the sum of the angle of triangle is 180 degree isliye from ∆abc, we have angle 2 + angle 4 + angle b= 180°, from angle ACD ,we have angle 1 + angle 3 + angle d =180°, adding angle either side we get 360°

Answer 2

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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°.