Prove that the sum of the angle of a quandrilateral is 360
Answers
Answer:
it is having 4 sides
so
4x=360
x=360/4
x=90
it means they are sharing into equal parts
so
the sum of the angle of a quandrilateral is 360
Step-by-step explanation:
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Answer: The sum of the angles of quadrilateral is 360 is proved
The diagram for this sum is attached below
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°.
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°.