Question

Prove that sum of interior angles of a quadrilateral is 360degree

Answer 1

$\underline\bold{Answer}$

★ Given

ABCD is a quadrilateral

★ To prove

∠A + ∠B + ∠C + ∠D = 360°

★ Construction

Join AC

★ Proof

There are two triangle △ ABC & △ADC

We known that Angle sum property of a triangle is 180°

Therefore,

△ ABC + △ADC = quadrilateral ABCD

180° + 180° = quadrilateral ABCD

360° = quadrilateral ABCD

Hence proved,

∠A + ∠B + ∠C + ∠D = 360°