Question

Prove that sum of all angles of any quadrilateral is equal to two straight angle.​

Answer 1

Answer:

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Step-by-step explanation:

Let a,b,c,d be the angles of a quadrilateral.

We know that a+b+c+d=360 . (angles sum up to 360)

This means that a=360−(b+c+d) (subtract b+c+d on both sides)

Also, a>0 (since an angle cannot be 0 or negative)

It follows that 0<360−(b+c+d) , by substitution.

Adding b+c+d to both sides, we get

b+c+d<360

which means that angles b , c ,and d sum up to less than 360°, what we wanted to prove. Q.E.D.