Question

prove that the sum of the angles of the quadrilateral is 360°
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Answer 1

Answer:

Step-by-step explanation:

ANSWERED BY GAUTHMATH

Answer 2

1) If we draw one diagonal to quadrilateral we will get two triangles. i.e. △ ABC and △ ACD

But we know that sum of angles of triangle is 180°

Sum of angles of quadrilateral ABCD = sum of angles △ ABC + sum of angles △ ACD

⇒ 180° + 180°

⇒ 360°

Hence, It is Proved..!!

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2) Consider △ ABC We can write it as

∠CAB + ∠B + ∠BCA = 180° …….. (1)

Consider △ ACD We can write it as

∠DAC + ∠ACD + ∠D = 180° ……… (2)

Adding equations (1) and (2) we get

∠CAB + ∠B + ∠BCA + ∠DAC + ∠ACD + ∠D = 180° + 180°

So we get

∠CAB + ∠DAC + ∠B + ∠BCA + ∠ACD + ∠D = 360°

So it can be written as

∠A + ∠B + ∠C + ∠D = 360°