Question

prove that the sum of all angles of a quadrilateral is 360'​

Answer 1

Answer:

Hope this helps.

Draw in one of the diagonals.

This divides the quadrilateral into two triangles.

The sum of the angles in each triangle is 180°.

So the sum of the angles in the quadrilateral, being equal to the sum of the angles in the two triangles, is equal to 2 × 180° = 360°

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°.