Question

If the sides BA and DC of quadrilateral ABCD are produced as shown in the given figure. then
Refer Image

• A. x + y = a + b
• B. x - y = a - b
• C. $\frac{x-y}{2}=a-b$
• D. None of these

Answer 1

Answer: (A)

x + y = a + b

For Triangle CBD, $\angle a$ is exterior angle.
So, $\angle 1+\angle 2=\angle a$ -----------eq1
& For Triangle ABD, $\angle b$ is exterior angle.
So, $\angle 3+\angle 4=\angle b$-----------eq2
adding eq 1 and eq 2
$\angle 1+\angle 2+\angle 3+\angle 4=\angle a+\angle b$ (As $\angle 1+\angle 4=\angle x$ & $\angle 3+\angle 2=\angle y$)
So,
$\angle x+\angle y=\angle a+\angle b$
Answer (a) x + y = a + b