Question

prove that sum of angke of quadrilateral is 360​

Answer 1

Answer:

In the quadrilateral ABCD,

∠ABC, ∠BCD, ∠CDA, and ∠DAB are the internal angles.

AC is a diagonal

AC divides the quadrilateral into two triangles, ∆ABC and ∆ADC

We have learned that the sum of internal angles of a quadrilateral is 360°, that is, ∠ABC + ∠BCD + ∠CDA + ∠DAB = 360°.

let’s prove that the sum of all the four angles of a quadrilateral is 360 degrees.  

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

Now consider triangle ADC,

∠D + ∠DAC + ∠DCA = 180°                           (Sum of angles in a triangle)  

Now consider triangle ABC,

∠B + ∠BAC + ∠BCA = 180°                            (Sum of angles in a triangle)  

On adding both the equations obtained above we have,

(∠D + ∠DAC + ∠DCA) + (∠B + ∠BAC + ∠BCA) = 180° + 180°

∠D + (∠DAC + ∠BAC) + (∠BCA + ∠DCA) + ∠B = 360°

We see that (∠DAC + ∠BAC) = ∠DAB and (∠BCA + ∠DCA) = ∠BCD.

Replacing them we have,

∠D + ∠DAB + ∠BCD + ∠B = 360°  

That is,

∠D + ∠A + ∠C + ∠B = 360°.

HENCE PROVED

Step-by-step explanation:

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