Question

Prove that the sum of intterior angles of a quadrilateral is 360 degree

Answer 1

Step-by-step explanation:

The sum of the measures of the interior angles of any quadrilateral can be found by breaking the quadrilateral into two triangles. Since the measure of the interior angles of any triangle equals 180 degrees, each of the two triangles will contribute 180 degrees to the total for the quadrilateral.

So the measure of the interior angles of a convex quadrilateral is the same as the sum of the measures of the interior angles of two triangles, or 360 degrees.

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°.