Question

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

Answer 1

Step-by-step explanation:

Proof: Let ABCD be a quadrilateral. Join AC.

Clearly, ∠1 + ∠2 = ∠A ...... (i)

And, ∠3 + ∠4 = ∠C ...... (ii)

We know that the sum of the angles of a triangle is 180°.

Angle Sum Property of a Quadrilateral

1Save

Therefore, from ∆ABC, we have

∠2 + ∠4 + ∠B = 180° (Angle sum property of triangle)

From ∆ACD, we have

∠1 + ∠3 + ∠D = 180° (Angle sum property of triangle)

Adding the angles on either side, we get;

∠2 + ∠4 + ∠B + ∠1 + ∠3 + ∠D = 360°

⇒ (∠1 + ∠2) + ∠B + (∠3 + ∠4) + ∠D = 360°

⇒ ∠A + ∠B + ∠C + ∠D = 360° [using (i) and (ii)].

Hence, the sum of all the four angles of a quadrilateral is 360°.

Answer 2

Answer:

The sum of the measures of the interior angles in any convex quadrilateral is 360 degrees. .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.

Step-by-step explanation:

Plz follow me friend and mark this answer as a brainlist answer plz