Question

The sides $BA$ and $DC$ of the quadrilateral $ABCD$ are produced as shown in the figure, then ___________.

• A. $a+x=b+y$
• B. $a+y=b+x$
• C. $a+b=x+y$
• D. $a+b=x-y$

Answer 1

Answer: (C)

$a+b=x+y$

In quadrilateral $ABCD$,

$\angle A=180-b$

and $\angle C=180-a$

Sum of all the angles of a quadrilateral is:

$\angle A+\angle B+\angle C+\angle D={360}^o$

$\Rightarrow 180-b+x+180-a+y=360$

$\Rightarrow 360-a-b+x+y=360\Rightarrow a+b=x+y$