Question

prove that the sum of the angle of a quadrilateral is equal to four right angle​

Answer 1

Given:

The sum of the angle of a quadrilateral is equal to four right angle​

To find:

Prove that the sum of the angle of a quadrilateral is equal to four right angle​

Solution:

From given, we have the data as follows.

Let ABCD be a quadrilateral.

Construction: Join AC.

From the figure it's clear that,

∠1 + ∠2 = ∠A ...... (i)

And, ∠3 + ∠4 = ∠C ...... (ii)

w.k.t. the sum of the angles of a triangle is 180°.

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°, that is, four right angle​ .

Answer 2

Answer:

First ka answer is right ha