Question

Prove that the sum of the angles of a quadrilateral is 360 degree . ​

Answer 1

Answer:

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░▒▓█ Hello █▓▒░

Proof: 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°.

Or, the sum of angles of a quadrilateral is 360°. This is the angle sum property of quadrilaterals

Answer 2

HEY MATE!

I'm Sneha Bajaj and the answer u want is given below:-

Q1:-Prove that the sum of the angles of a quadrilateral is 360 °

Ans:

GIVEN:-

ABCD is a quadrilateral with 4 sides

WE HAVE TO PROVE:-

Sum of angles is of a quadrilateral is 360° also known as angle sum property of quadrilateral

CONSTRUCTION :-

Draw a line AC in the quadrilateral ABCD

PROOF:-

As we know sum of all angles of a triangle Δ is 180° then,

ΔADC + ΔABC= ABCD

180°+180°= ABCD

360° = ABCD

HENCE PROVED THAT THE SUM OF THE ANGLES OF A QUADRILATERAL IS 360°.

HOPE IT HELPS

THANK YOU ☆