Question

Proof of the sum of the angles of quadrilateral is 360 degree

Answer 1

Answer:

Step-by-step explanation:

Theorem and Proof of angle sum property of a quadrilateral. Prove that the sum of all the four angles of a quadrilateral is 360°. Proof: Let ABCD be a quadrilateral. ... We know that the sum of the angles of a triangle is 180°.

Answer 2

Question:Sum of the angles of quadrilateral is 360°

Given:

A quadrilateral ABCD

To prove:<A+<B+<C=360°

Construction:Join BD

Proof:Since the sum of the angles of a triangle is 180°

we have

<A+<1+<2=180°. {sum of <s of ∆ABD}

and <3+<C+<4=180° {sum of <s of ∆BCD}

On adding i) and ii)

<A+<1+<2+<3+<C+<4=180°+180°

as <1+<3=<B and <2+<4=<A

<A+<B+<C+<D=180°+180°

<A+<B+<C+<D=360°

Proved