Prove that the sum of the angles of a quadrilateral is 360°.
Answers
Answer:
A quadrilateral is a polygon which has 4 vertices and 4 sides enclosing 4 angles and the sum of all the angles is 360°. When we draw a draw the diagonals to the quadrilateral, it forms two triangles. Both these triangles have an angle sum of 180°. Therefore, the total angle sum of the quadrilateral is 360°.
Answer:
can 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.
Mate i tried my best plz mark if you can, No copied answer : )
